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Joe Pagano - EzineArticles.com Expert Author
Joe is a prolific writer of self-help and educational material and an award-winning former teacher of both college and high school mathematics. Under the penname, JC Page, Joe authored Arithmetic Magic. As a result of this publication, Joe was invited to be a guest on the television show the Book Authority. Joe is also author of the charmingly pithy and popular ebook, Make a Good Impression Every Time: The Secret to Instant Popularity; the ... [More]
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- Why Study Algebra? - Special Products - The Sum and Difference of Two Cubes
[Reference-and-Education] There are two special products in algebra that are worthy of mentioning: the sum and difference of two cubes. Although the quadratics are much more common, the cubes and indeed higher order polynomials find their place in all sorts of interesting applications. For this reason, learning to factor x^3 + y^3 and x^3 - y^3 deserve some attention. Let us explore them here.
- How I Became a Mathematician - It's Not As Serious As You Think
[Reference-and-Education] I don't know. I guess it all happened back in high school when a friend of mine called out in algebra class how much he hated logarithms. After that remark, I figured I was in for trouble as I was your average Sylvester Stallone look-alike, and certainly not what you would consider the "math nerd" type.
- Why Study Algebra? Completing the Square It's Not As Hard As You Think
[Reference-and-Education] One of the most useful techniques in algebra is that of completing the square. The name is appropriate as the geometric interpretation encompasses the formation of a square from a rectangle by the addition of an appropriate quantity. Geometry aside, this technique has many applications, not only in algebra, but also in more advanced realms such as integration, which is a key component of integral calculus. Here we will see that this technique can be had rather inexpensively.
- Mastering Algebra - Recognizing Special Products and Their Factors - Part I
[Reference-and-Education] One of the key difficulties in algebra is learning to recognize special products and their respective factors. For example, the special polynomials which are formed by the difference of two perfect squares and perfect square trinomials have standard factors which can easily be obtained once one recognizes...
- Trigonometry For Dopes - The Sine and Cosine
[Reference-and-Education] Trigonometry is hailed as a rough subject, particularly for precocious high school students brave enough to wade into its potentially turbulent waters. Notwithstanding "trig" challenges, the key to mastering this subject really lies in the basic understanding of its two key players: the sine and cosine. All the other features of this fascinating subject really derive from the shenanigans that these two play on unsuspecting students. Consequently, before students plunge into this mysterious realm of triangular measurement and other identities, they should make sure they are intimately familiar with its two key players and the critical roles they play.
- Mastering Algebra - Recognizing Special Products and Their Factors - Part II
[Reference-and-Education] Now that we understand some key algebraic terminology, we are prepared to recognize some special products and to be able to factor them accordingly. Herein we master how to recognize and factor both differences of perfect squares and perfect square trinomials.
- Mathematics, Numbers, and The Symmetry of God
[Reference-and-Education] The essence of mathematics is not to make simple things complicated, but to make complicated things simple. - S. Gudder. Indeed mathematics is a domain where brains get rankled and minds seem to lose their grips on reality. Yet in this seemingly mad world, simplicity metamorphoses from complexity; normality evolves from irrationality, and order blossoms from chaos. If you doubt these propositions, then observe the bizarre symmetry in the following numerical calculations, and then see whether you are still skeptical that God does in fact indwell numbers and mathematics.
- School's Back - Are Your Kids Ready?
[Kids-and-Teens] September lurks around the corner while the kids are trying to squeeze every last drop out of summer fun. With September comes back to school and for most kids that means getting up early to attend class, doing homework assignments and projects, maybe hitting the library for the really ambitious, and of course no more late nights on the computer-at least we parents hope.
- Why Study Math? - Solving Multi-Step Linear Inequalities - Part II
[Reference-and-Education] As we discussed in Part I, multi-step linear inequalities are quite easy to solve. Essentially, the steps involved are much like those used to solve an equation. There is one situation, however, in which the technique to solve an equation and inequality differ and that is when we multiply or divide by a negative number. The reason for this will become clear as you read on.
- In Mathematics There is No Hypocrisy
[Reference-and-Education] Mathematics is rife with beauty. Yes beauty. Oh, maybe not the type of physical beauty you are thinking of but a beauty that can only be perceived when you study this subject in all of its fabulous environs. One particular beauty that hooks me to this discipline like no other is that of being without hypocrisy. That's right. In mathematics there is no hypocrisy.
- Holy Yoli! Feeling Good and Getting Better
[Health-and-Fitness:Supplements] Every now and then, something so good comes along that it behooves us as human beings to spread the word so that all can share in the good fortune. Such is the case with the apparent health promoting benefits of acai, pomegranate, and above all resveratrol. Science is showing that there is a correlation between taking these substances and better health. People are starting to look and feel younger everyday, so why shouldn't you?
- Amazing Numbers - The Fractions Are Dense But the Reals Are Even Denser
[Reference-and-Education] Numbers are the foundation of all mathematics and numbers are the ticks to the mathematical clock. Maybe I'm just strange but numbers never cease to amaze me. What kinds? All kinds. You have the natural numbers, the integers, the fractions, and the reals; and these last two really never cease to impress me because of their mystical properties.
- Why Study Math? - Solving Multi-Step Linear Inequalities - Part I
[Reference-and-Education:Science] Unlike an equation, which shows balance or harmony among two expressions, an inequality shows imbalance. That is, an inequality states that one expression is bigger than or less than another expression. Linear inequalities involve expressions which are lines, or linear equations. These inequalities are solved much the same way as equations with one key difference. Read on to enter this curious world.
- Why Study Math? - A Lesson in Predation - Does the Cheetah Catch the Gazelle?
[Reference-and-Education] Imagine that you are a hungry cheetah grazing out on the savannah in Africa. The sun is blazing overhead at a cool 110 degrees Fahrenheit and because of the recent heat you have been unable to locate any prey to eat because they have all been hiding out in some cool shade somewhere. Suddenly off in the distance you espy a delicious looking gazelle. You know it is hot, but you have one last burst of energy. You know you can run up to 60 miles per hour. The catch looks possible. The question is, do your calculations make sense? because if they don't, you don't get to eat once again.
- Math and Twitter - What's the Tweet?
[Internet-and-Businesses-Online:Social-Media] Social networking platforms are popping up faster than you can say "twitter." So now besides checking your text messages on your mobile phone, your three or so email accounts, you must check your facebook page, your myspace page, and of course your twitter account.
- Math and Cooking - Know Thy Fractions
[Food-and-Drink:Cooking-Tips] Knowing math has afforded me countless advantages in life which would be too numerous to mention here. Aside from feeling more adequate in everything I do, math gives me the edge when it comes to problem solving, strategizing, planning, and yes even cooking! In the recipe above, the problem becomes one of scaling down the ingredients to accommodate 4 chicken breasts instead of 6. In terms of fractions, this means that you have 4/6 or 2/3 of the required chicken. To adjust the recipe so that everything stays in the same ratios, we need to take 2/3 of the other ingredients. Ah, fractions those devils!
- How to Succeed in Algebra - Factoring Non-Monic Trinomials - Part II
[Reference-and-Education] In Part II of this article, we are going to examine a sure-fire way to factor non-monic trinomials. We are going to examine the proof which gives us this powerful method. After you are done with this presentation, you will not only be able to factor any non-monic, you will understand the reason why this method works.
- How to Succeed in Algebra - Factoring Non-Monic Trinomials - Part I
[Reference-and-Education] One of the stumbling blocks for students in algebra is factoring what is known as non-monic trinomials. Simply stated a non-monic trinomial is one of the form ax^2 + bx + c, in which a is greater than 1. These present a challenge in factoring because the traditional "guess-and-check" method produces too many possibilities to try. The approach outlined in this series of articles will not only show the fail-proof way of slaying these trinomials but also give the reason, or proof, as to why this method is valid.
- Your Son Or Daughter Can Be a Whiz Kid Too
[Reference-and-Education:Online-Education] So do you think as a mom or dad that the prestigious status of whiz kid, accorded to children with outstanding mathematical abilities, is reserved for the other parent's children? Well think again. My bold claim is that any child can be accorded such privileged status provided that he has an interested parent and that the process of acquiring this status is begun early, preferably during the early pre-teen years.
- Teach Your Kids Arithmetic - Multiplication Shortcuts Part II
[Reference-and-Education] Did you ever watch an illusionist pull off one of those amazing mind-blowers in which a rabbit appears out of a seeming empty hat? Or one in which, a previously torn piece of paper with unique writing on it is miraculously restored whole? These mind-bending illusions might really seem like magic but there is a trick behind every one. Similarly with math, multiplying lightning fast might seem like an illusion, but there really is a trick behind it. With various shortcut techniques, some of which will be outlined here, you too can seem like a mathematical illusionist.
- The Earned Run Average (ERA) In Baseball - Nothing More Than a Complex Fraction
[Recreation-and-Sports:Baseball] Now that baseball season is well under way, many of you might be wondering how that statistic called the earned run average (era) is computed. You might know that this stat reflects a pitcher's allowed, or earned, runs per nine innings. But did you know that this stat is nothing more than a complex fraction in mathematics and can be calculated with a nice little trick?
- Why Study Calculus?
[Reference-and-Education] As part of a subcategory within my "Why Study Math" series, I am pleased to introduce a new group or articles that will touch upon some of the higher branches of mathematics. The purpose of these writings will be to introduce people-particularly the lay person-to some of the more advanced reaches of this subject. Many people unfortunately never get to glimpse the fascinating beauty of the higher realms of mathematics such as the Calculus, and far too many are under the mistaken belief that this field is only reserved for the so called erudite and genius crowd. Not so I say. Give me a chance and I will be happy to accommodate you.
- And You Thought Fractions Were Hard?
[Reference-and-Education] Fractions as you know are formed by taking the quotient of two integers. Thus 1/2 and 4/5 are fractions because they are formed by the quotients of 1 and 2, and 4 and 5, respectively. Fractions are a real headache for most students of math, and the arithmetic of fractions-particularly addition and subtraction-has been known to cause many a student's nightmare. Yet as troublesome as these beasts are, take heart: there are worse mathematical monsters out there.
- Math Tricks Equal Educational Success
[Reference-and-Education:Online-Education] "Numbers are the highest degree of knowledge. It is knowledge itself." -Plato As the quote elucidates, knowledge sits on the shoulders of numbers. Whenever I encounter a quote like this, particularly when the source is as renowned as that of the likes of Plato, I sit back and muse smugly that I hit the nail on the head many years ago when I realized that numbers were indeed the highest degree of knowledge. Extrapolating from this realization, we can say with certainty then that learning to work with numbers as through math tricks and such-that is, getting an inner feel for all their intricacies and richness-will produce extraordinary results in the education of any man, woman, or child.
- Mathematicians and Poets - Two of a Kind?
[Reference-and-Education:Online-Education] "A mathematician who is not also something of a poet will never be a complete mathematician." -- Karl Weierstrass C'mon a mathematician who's a poet! Give me a break. Isn't that as compatible as a snake and a mongoose? You mean there really is some truth in the quote by Weierstrass, one of the most famous mathematicians of all time, who is probably responsible for the rigors of calculus? Indeed mathematics has a rhythmic structure which, when probed, reveals its poetic and musical beauty. And any person who masters this discipline rightfully then should be regarded as something of a poet.
- Why Study Math? - The Fibonacci Sequence and Sex Appeal
[Reference-and-Education] Oh, that field of math. Don't you just love to hate it? Yet you have to admit that when someone explains some of its beauty to you and you get it, you marvel at how amazing a field it actually is. Such is the case with number sequences and in particular one called the Fibonacci sequence. For those who do not know what a sequence is, it is simply a list of numbers that follow some predefined rule. For example, the sequence 2, 4, 6, 8 is the arithmetic sequence which is defined by multiples of the number 2. The Fibonacci sequence is the following: 1, 1, 2, 3, 5, 8, 13...Do you see the pattern?
- Why Study Math? Using Lines to Make Predictions
[Reference-and-Education] Lines in math can be expressed various ways using equations. Each equation is called a linear model. Here, we are going to examine why it is even worth our time to learn about such models and their representative equations. After this investigation, we will come to understand the power of these seemingly innocent and simple mathematical entities.
- Why Study Math? - Pascal's Triangle and the Binomial Theorem - Part II
[Reference-and-Education] In Part II of this article, I discuss how you use Pascal's Triangle to expand a binomial to the fourth power. In particular, we examine...
- Mathematics and Let's Make a Deal - What's Behind Door Number 1?
[Reference-and-Education] Suppose you had the chance to be on the famous 1970's game show "Let's Make a Deal" which was hosted by the genial and oft witty Monty Hall. You are given a choice of three doors to select from, behind one of which is a new car. You select door Number 1. The witty Monty Hall decides to open up door Number 2 to reveal a goat. He now gives the chance to switch your door selection. The question is do you switch or stay with your original selection? Well a knowledge of mathematics, and in particular variable change, tells you what to do.
- The Benzene Ring and Math - What's the Scoop?
[Reference-and-Education] For those of you chemistry students out there, you know that the benzene ring is one of the most prevalent ring structures found in organic chemistry, and this chemical compound finds itself involved in many chemical reactions and even enmeshed in the ring structures of innumerable organic compounds. Moreover its versatility as a chemical reagent allows it to be used to synthesize drugs, plastics, gasoline, synthetic rubbers and dyes. So what does this have to do with math and in particular geometry?
- Teacher Pay - Fair and Balanced?
[Reference-and-Education] With a new President-Elect and the coming of a new administration, education will be a key issue in the coming years. For many teachers out there, the topic of professional compensation is a hot item. For years, politicos have been pushing agendas to try to reform teacher pay so that an educator's compensation was more in line with other mainstream professionals. The question is, "How do we make teacher pay fair and balanced, while insuring that we are not overcompensating the weak links in the chain?"
- Why Study Math? - Pascal's Triangle and the Binomial Theorem - Part I
[Reference-and-Education] Many times in mathematics we find a fascinating relationship between two different objects. Such is the case with a curious triangle and the coefficients of a specific expression. The curious triangle is called Pascal's Triangle, eponymously named after the famous French mathematician, and the specific expression is a binomial expansion, obtained by raising a binomial to an integral power.
- Mathematics - Beautiful For Many Reasons
[Reference-and-Education] Mathematics is rife with beauty. Yes beauty. Oh, maybe not the type of physical beauty you are thinking of but a beauty that can only be perceived when you study this subject in all of its fabulous environs. Whether it be the elegance of a particular formula or the economy of expressing something very complicated in a concise way, mathematics trumps the field of aesthetics in a manner worthy of praise.
- Calculus For Dopes - It's Not That Hard - The Antiderivative
[Reference-and-Education] If you are of the belief that everything has an opposite, then when it comes to the calculus you are absolutely right, in that the derivative has its very own opposite: the antiderivative. The process of taking the derivative of a function is known as differentiation. The process of going from the derivative back to the original function is known as "antidifferentiation," or integration. Both processes have important applications in mathematics, and, by extension, the real world.
- Why Study Math? - How About Solving Rubik's Cube?
[Reference-and-Education] So you think that math does not teach you things like solving Rubik's cube? Then think again. My ability to figure out the 3x3 cube lies not so much in my inherent brilliance but because my mathematical training taught me how to problem solve and to figure out things that without such training, I would never have figured out, or even attempted. Not that the Rubik's cube is as difficult as the Einstein Field Equations, but with 43 quintillion possibilities, it is certainly no walk in the park either. Mathematics helped train me to tackle this brain buster.
- Why Study Math? - Group Theory and Subparticle Physics
[Reference-and-Education:Science] In the field of abstract algebra, a mathematical entity called a group plays a key role that resonates throughout the fascinating meadows of this intriguing discipline. Still more fascinating is that the theory of this mathematical creature, or "group theory," was thought early on by mathematicians to have only intellectual appeal. That is, nobody in his right mind thought that the group and its concomitant theoretical aspects would ever serve mankind in any way other than to stimulate his cognitive awareness. Yet as irony would prove, the mathematical group would prove to be the pathway to understanding particle physics and the subatomic entities that spin the tales of this most curious science.
- Why Study Calculus? - Related Rates
[Reference-and-Education] One of the more interesting applications of the calculus is in related rates problems. Problems such as these demonstrate the sheer power of this branch of mathematics to answer questions that would seem unanswerable. Here we examine a specific problem in related rates and show how the calculus allows us to come up with the solution quite easily.
- Why Study Math? - Functions and Rules
[Reference-and-Education] One of the most important concepts in mathematics is that of a function. Although the topic of function can appear abstract, it is nothing more than a specific rule between two sets of mathematical objects. These sets are usually numbers, but they do not have to be restricted to such mundane entities. The sets might consist of more interesting objects, such as matrices or vectors. This notwithstanding, a function is nothing more than a rule that associates with each member of one set another member of the other set. Here we discuss this exciting concept in a little more detail so that the next time you see or hear about it, you do not avert your eyes or go cowering away in fear instead of joining in on the conversation.
- Numbers - How Big is Big?
[Reference-and-Education] The Natural Numbers form the set of numbers beginning with 1 and sequentially adding 1 to go 1,2,3,... ad infinitum. Although infinite, the Natural Numbers do not display an infinity as "big" as that of the real numbers; however, they are certainly big enough to permit the counting of very large quantities: to wit, the distances in miles between stars, and the number of sand grains on a given beach. Yet as big as the previous quantities might be, we can think of still larger quantities. So how big is big?
- Why Study Calculus? - Volumes of Irregular Shapes
[Reference-and-Education] Sometimes it would seem that learning mathematics is hardly worth the effort. All those painful techniques and formulas, replete with grotesque and hideous symbolism, would detract even the heartiest from diving headfirst into this strange world. Yet when you come to understand that such arcane features actually serve purpose, you begin to realize that mathematics solves very difficult problems with an economy that would make the most niggardly cheapskate proud. Such is the case with calculus. Here we look at how this discipline allows us to calculate the exact volume of some very bizarre shapes.
- Teachers, Teach - Don't Preach!
[Reference-and-Education] The crisp dry September air is hurtling around August' corner, and you can feel, taste, and smell the first days of school, looming tantalizingly behind that inspiration you received during the quickly fading summer. Yet inspired though you may feel, you still cannot overcome the frustrations of last year, when student apathy and lack of interest in your goods made teaching day to day seem like an eternity. What can you do, you ponder, to make this year different? How can you motivate your students, both the slackers and the hackers? Maybe some simple advice holds the answer.
- Why Study Math? - Bruce Lee Would Be Proud
[Reference-and-Education] Interesting how a fighting technique using the nunchaku weapon, the octagonal oak sticks connected by a short chain or string, which were immortalized by Bruce Lee in his famous martial arts film, "Enter the Dragon," and mathematics, particularly parametric equations, could be so nicely entwined. It is as though mathematics has no favoritism when popping its head up in all kinds of seemingly unrelated fields. Read on and you will see how the nunchaku and math are so related.
- Why Study Math? - Parametric Equations
[Reference-and-Education] Math abounds with confusing topics. From arithmetic to algebra to calculus and beyond, there always seems to be some topic that creates confusion, even in the hardiest of students. For me, parametric equations was always one of those topics. But as you will see in this article, these equations are no more difficult than arithmetic.
- Why Study Math? - Solving Linear Systems by Linear Combinations
[Reference-and-Education] Now that we have seen how to solve a system of linear equations using the substitution method, we move to a more convenient method known as linear combinations. With this method-also known as addition-subtraction-we eliminate one of the variables by adding an appropriate multiple of one of the equations. We can then eliminate one variable and solve for the other. Once done, we use the other equation to solve for the other variable.
- Prime Numbers And The Fundamental Theorem of Arithmetic
[Reference-and-Education] Just as atoms are the building blocks of elements, prime numbers are the building blocks of arithmetic. This comparison becomes justified when we consider that all composite numbers can be uniquely generated by a specific product of primes. This last statement is one of the most important in number theory and is known as the Fundamental Theorem of Arithmetic.
- Why Study Math? Linear Systems and the Substitution Method - Part II
[Reference-and-Education] As we are quickly learning from my series of articles on lines and their applications, the power of these mathematical objects should not be taken for granted because of their simplicity. Lines and more specifically, linear systems, find important applications in the fields of telecommunications, signal processing, and automatic control, the last field of which deals with such interesting things as the programming, guidance, and control of ballistic missiles. In the first article in this series, we examined how to solve a linear system by the method of substitution. Here we will look at some basic problems which employ such linear systems.
- Why Study Math? Linear Systems and the Substitution Method - Part I
[Reference-and-Education] After having read my previous articles on lines and their representative equations, we are now going to look at these objects two at a time, in which case we have what is known as a linear system. When we have two lines, and we try to graph them on the same coordinate plane, three things can happen: one, the lines may never intersect, in which case they are parallel; two, the lines may coincide, in which case they are identical; or three, the lines can intersect in one point, the unique solution of the system. Here we are going to look at how to find that unique solution using the method known as substitution.
- Why Study Math? Linear Equations and the Point-Slope Form
[Reference-and-Education] As we saw in the article"Why Study Math? - Linear Equations and Slope-Intercept Form," linear equations or functions are some of the more basic ones studied in algebra and basic mathematics. Here we are going to take a look at and examine another common way of writing linear equations: the point-slope form.
- Why Study Math? Linear Equations and Slope-Intercept Form
[Reference-and-Education] Linear equations or functions are some of the more basic ones studied in algebra and basic mathematics. The import of these functions is that they model many real world phenomena and a key component of them, the slope, is a springboard concept for the realm of the calculus. That's right: the basic idea of rise over run, or slope, within these equations, leads to all kinds of interesting mathematics.
- If At First You Fail, Remember Many Great Ones Before You Did Also
[Self-Improvement:Motivation] If you have tried and failed, fear not: many great ones before you have experienced this fortune. What is important is not whether you have failed, but what you have done after such failure. Did you feel sorry for yourself and give up all hope of success? Or did you dust off the sweat and blood, and vow to come back stronger, and eventually win the prize? Depending on your course of action, you may end up another casualty of the ne'er-do-well society, or you just might end up making your mark on life.
- Advanced Mathematics - What Does it All Mean?
[Reference-and-Education] If you think mathematics is a difficult subject, you should try studying some of the more advanced branches like abstract algebra before you come to such a conclusion. It is in these higher realms of this most distinguished subject that one learns about mathematical structures like groups, fields, and rings, and the properties inherent in these objects. After a jaunt through such mysterious realms, one comes away with a new appreciation of this most fascinating subject.
- Teach Your Kids Arithmetic - Mastery of the Multiplication Table
[Reference-and-Education] Learning your multiplication facts does not have to be hard. In fact, depending on how you look at it, this feat can be quite fun. Repetition does play a role, but knowing some cool tricks can be the difference between success and failure. So why struggle with multiplication when mastering this arithmetic operation can be yours easily? Here you get the key to mastery of the most important table you will ever learn.
- School Administrators - Get Off Your Teachers' Backs!
[Reference-and-Education] School administrators, do your teachers a favor and get off their backs and let them teach. This is especially true for the non-tenured teachers, and the ones that really have their hearts in the profession. Yes, we all know you administrators have a job to do. But do us all-and indeed the country-a huge favor: worry about more serious things like violence and drug abuse in your schools and less about what kind of classroom management skills your teachers have.
- Teach Your Kids Arithmetic - Multiplication Shortcuts - Part I
[Reference-and-Education] When Gauss said that mathematics was the queen of sciences and arithmetic the queen of mathematics, he was not lying. Without arithmetic, there could be no mathematics; for the essence of this most challenging discipline lies in the ability to manipulate numbers and figures. Multiplication, division, addition, and subtraction form the core of arithmetic operations. In this article, we will examine some niceties regarding the first of these four operations.
- Trigonometry for Dopes - The Touchy Tangent
[Reference-and-Education] The tangent is the last of the three principal trigonometric functions. It derives its name from the Latin tangere for "to touch." This derivation is relevant to the actual mechanics of the function and the manner in which the tangent works to give us some important measurements in life. You see, the tangent allows us to compute the maximum and minimum values of a function, and this application has significant weight in the real world.
- Trigonometry for Dopes - The Sine's Better Half
[Reference-and-Education] If you read the first article in this series, then you know the sine is an important trigonometric function. Yet as important as the sine is, and as myriad the formulas and mathematical laws that it finds itself entwined in, one finds in the study of trigonometry an equally formidable ally: the cosine.
- From Fractions to Calculus
[Reference-and-Education] So you want to learn higher math? Calculus, you say? Well, let me state right here and now that if you don't master fractions, guess what? Did I hear what I think you said? Yes, that's right. You will never learn calculus.
- Homeschooling - Do It Right or Don't Do It At All
[Reference-and-Education:Home-Schooling] When it comes to homeschooling your son or daughter, it is important to realize that you are assuming a huge responsibility in the shaping and molding of his or her education. You really do not have that much time or flexibility to try out a hundred different approaches and programs until you hit on the right one. You need to have some guiding mechanism which insures that you are achieving your objectives. If you don't, the one who suffers is your son or daughter.
- Trigonometry for Dopes - What's Your Sine?
[Reference-and-Education] Trigonometry is a word which derives from the Greek, meaning "measure of triangles." Its origins can be traced back to early Mesopotamia where sailors and navigators invented this discipline to help determine position and location. To think an act so simple as the measurement of triangles and the study of relationships between its angles and sides could harbinger the development of a mathematical discipline which in turn would find itself involved in such diverse fields as astronomy, navigation, music theory, acoustics, optics, electronics, economics, number theory, pharmacy, chemistry, geodesy, cartography, crystallography, architecture, oceanography, engineering, game theory, ultrasound, cryptography, meteorology, seismography, medical imaging (i.e. CAT scans), phonetics, statistics, and biology, to name a few-then you have thought rightly.
- Why Study Math? Trigonometry and SOHCAHTOA
[Reference-and-Education] Trigonometry is that curious branch of mathematics that deals with the measurements and relationships of the various triangles and their sides and angles. It would appear hard to imagine that so seemingly unglamorous a discipline as this would find itself intertwined in so many physical applications of the world around us and in many branches of physics and upper mathematics. Yet this is indeed the case.
- Start the Year Right - Work Your Brain
[Self-Improvement:Techniques] Now that the New Year is upon us it's time to start putting all those creative resolutions into action. Do you want this year to be a same boring repeat of last year or do you want to make those changes that will really impact your life in a positive way? Even if last year was a good one, it's time to make this one an even better one. Let's start by resolving to work our brains so that all the other things fall into place.
- So How Smart Are You Really?
[Self-Improvement:Success] Why is being smart so important? And of the two, being smart or being beautiful, which one ranks first? What if you are one of the lucky ones that is both smart and beautiful-and what if you are also rich? God, some people are so darn lucky! Really, being smart is considered an important attribute and most people would never admit to being anything less. So how do we determine whether you are smart or not, and if you pass muster, how do we rank you by degree of smartness?
- Materialism - How Much is Enough?
[News-and-Society:Economics] How materialistic our children have become never ceases to amaze me. Did you ever look at what our children want and desire and how much these things cost? Ed Hardy is making a killing marketing to our kids and so is Michael Jordan with his never ending barrage of new-release Air Jordans. How much is enough? What happened to the days of $2.95 Converses and $5 Levi Jeans? No wonder our country is in the mess it is.
- Making Money Fast - The Secret Is There Is No Secret
[Self-Improvement:Success] You've read hundreds of the self-help books, in which the gurus tout a thousand ways to make money and become an almost instant millionaire. The internet is littered with hundreds - yes thousands - of programs that promise incomes of thousands per day, even per hour. You were gullible enough to sign up and purchase some of these supposed "wealth-panaceas." Yet you're still living paycheck to paycheck. How come? Read on.
- Why Study Math? - The Mathematics of Finance - Calculating Your Mortgage Payment
[Reference-and-Education] In the first two parts of this series we discussed how compound interest is computed and the effects of various compounding on your net return. Here we discuss how that dreaded of all dreaded payments is calculated. What is it? - yes, you got it, that death pledge of a debt - the mortgage. You'll want to read this.
- Why Study Math? - The Mathematics of Finance - Interest - Part II
[Reference-and-Education] In the first part of this article series on the mathematics of finance, we discussed the compound interest formula and how it is used to calculate the accumulated value of money deposited over time. In this next part, we examine the different methods of compounding and the impact this has on the growth of your money. The interesting thing of all this compounding stuff is that you will see that regardless of how frequently we compound, at some point we reach an upper limit. In other words, frequent compounding helps but at some point you have to do more than just leave your money with "Frequent Compounding Bank USA" to get more of a return. Keep reading.
- Why Study Math? - The Mathematics of Finance - Interest - Part I
[Reference-and-Education] All right kids. So you hate math and you don't care whether you do well in this subject or not. But know one thing. Mathematics is the language of money. That's right. Whether we're talking interest on CD's or bonds, dividend yields on stocks, or returns on investment for a business venture, math is the lingua franca-or universal language. So remember that if you don't learn math well, you just might be giving an opportunity to some other hungry kid who wants to own more Jordan sneakers than you. Simply put: if you want the goodies in life, you best learn now that math can lead you to the land of fruit and nuts.
- Algebra for Dopes - It Ain't That Hard - Absolute Value Part IV
[Reference-and-Education] The last of this series deals with those absolute value inequalities which are greater than some other value. These inequalities fall under the disjunctive case because the graph of these produces two distinct regions on the number line. In other words, the regions are separated by the area in between, and because of this separation we give these inequalities the name "disjunctive," or separate. As you will see after reading this piece, these inequalities are quite simple to solve.
- Algebra For Dopes - It Ain't That Hard - Absolute Value Part III
[Reference-and-Education] With this article, we move into the realm of absolute value inequalities. Yuk! I can hear the groans now. Yet wait! These curiosity provoking creatures don't have to inflict as much pain as you think. So if you're worrying about you're next algebra test because the topic of absolute value inequalities will reign supreme, hang on to your hat and read the next two parts of this series of articles. You’ll be glad that you did.
- Algebra For Dopes - It Ain't That Hard - Absolute Value Part II
[Reference-and-Education] As we discussed in Part I of this series on absolute value, this topic is an absolute killer in algebra because of the choice that this concept presents. Absolute value can mean more than one thing, and as such, this duality of nature, so to speak, can wreak havoc on the less than intrepid warriors of algebra. However, if we break this concept down for what it really is, absolute value should never be a problem at all. You can then worry about the thousand and one other things in mathematics that are troublesome.
- Sudoku, Crossword Puzzles, and Math - A Lovely Trio
[Reference-and-Education] You know I have not yet caught on to the sudoku craze but from what I understand this puzzle game can become quite addictive. Maybe that’s the reason I havent dived in yet. You see, there is something delectably delightful about solving puzzles and other brain teasers and I simply have way too much to do already. Yet with all my busyness, I try to get in a good crossword or two from time to time, and I make sure to do some brain teasers. You should too and here’s why.
- Algebra for Dopes - It Ain't That Hard - Absolute Value Part I
[Reference-and-Education] One of the topics that is an absolute killer (no pun intended) in algebra and indeed higher branches of mathematics is absolute value. Yes that dreaded symbol "| |" of two straight vertical bars with some expression in between is usually enough to send shudders through most students. Yet this is not the way it has to be. You just need to know how to break this concept down into its bare components.
- Calculus for Dopes - It Ain't That Hard - The Limit Part II
[Reference-and-Education] In Part I of this series of articles, we introduced the concept of limit and discussed how this seemingly simple concept launched a branch of mathematics which would come to be known as the calculus. As we learned, the limit is nothing more than a value which is approached by a function when we let the independent variable become arbitrarily close to some value. Aside from defining the derivative-an essential function in all of calculus-the limit allows us to talk about things like division by zero. How strange!
- Calculus for Dopes - It Ain't That Hard - The Limit Part I
[Reference-and-Education] When Sir Isaac Newton was among other things working out the orbits of the planets in the 1600's, he realized that the mathematics of the day were simply-well-too simple. Thus he invented a new branch of mathematics called the calculus. What was different about this new math was that it enabled one to deal with "infinitesimals," or extremely small quantities. In fact, by virtue of these infinitesimals, mathematicians can calculate such things as the exact velocity of a moving body at any particular instant in time, or the exact area of a bizarrely irregular shape. The limit is one of the key aspects of calculus that allows us to do these extraordinary things.
- Don't Shoot Me, I'm Just The Math Teacher!
[Reference-and-Education] Yes, all you high school math teachers out there. The time has come for another year of teaching that dreaded of all dreaded subjects - math. No matter you teach basic math, algebra, or pre-calculus, the reaction of the students on that first day is always the same - fear. And because of the pain, you the math teacher, are going to inflict all year round on the students, with all those nasty tests, dreaded homework assignments, projects, and what-have-you's, those thirty or so pairs of eyes in that first class are going to drill you so deep on that first day that you are going to want to shout, "Don't shoot me, I'm just the math teacher."
- Algebra For Dopes - It Ain't That Hard - The Quadratic Equation - Part V
[Reference-and-Education] In Part V of this series, we examine how we solve the last class of factorable quadratics of the form ax^2 + bx - c, in which the b-term is positive and the c-term is negative. Such an example would be x^2 + 4x - 5. This subclass of quadratics are as easily solvable as those of the "bc-negative" class discussed in Part IV of this series.
- Algebra For Dopes - It Ain't That Hard - The Quadratic Equation - Part IV
[Reference-and-Education] In Part IV of this series, we examine how we solve factorable quadratics of the form ax^2 - bx - c, in which both the b and c terms are negative. Such an example would be x^2 - 4x - 5. This subclass of quadratics, which we will call the "bc-negatives," are easily solvable using the factoring techniques we learned about in Parts II and III of this series of articles.
- Algebra for Dopes - It Ain't That Hard - The Quadratic Equation - Part III
[Reference-and-Education] In Part III of this series, we examine how we solve factorable quadratics of the form ax^2 - bx + c, in which both the a and c terms are positive, but the b, or middle term, is negative. Such an example would be x^2 - 5x + 6. This class of quadratics, which we will call the "b-negatives" are easily solvable using the factoring techniques we learned about in Part II.
- Algebra for Dopes - It Ain't That Hard - The Quadratic Equation - Part II
[Reference-and-Education] As mentioned in Part I of this series, mastering algebra requires little more than clear-cut explanation and some concerted practice. Conquering the diverse aspects of this field necessitates focused thought and willingness to see through the trees to view the forest. Rather than view algebra - which encompasses many different topics and has vast extensions throughout - in one fell swoop, it is much better to view this subject piecemeal. This is the approach that will be taken in this series of articles.
- Great Teachers Don't Write Lesson Plans
[Reference-and-Education] When I think back to teaching high school, one of the most dreaded things was writing lesson plans. I realize now that great teachers should not have to write lesson plans. Great teachers should worry about teaching great lessons. Looking back, I realize I wasted a huge amount of time writing lesson plans that I never really used and ones that nobody really looked at. So why all the fuss?
- Algebra for Dopes - It Ain't That Hard - The Quadratic Equation Part I
[Reference-and-Education] When Persian mathematician al-Kwarizmi formulated the first algebraic principles, his purpose was to solve equations that up to his time were unsolvable by the methods then available. This math whiz doubtless was unaware that he would start a discipline which would thousands of years later cause all kinds of trouble for misguided high school students. Indeed the word algebra is derived from the word al-jabr, one of the two operations used to solve quadratic equations; and quadratic equations have enjoyed a royal romp of thousands of students throughout the ages since al-Kwarizmi's time. Yet it doesn't have to be this way.
- Your Kids Can Conquer Fractions
[Reference-and-Education] Your kids can learn to conquer fractions. The most important thing is that they not acquire an unnecessary fear of these tamable mathematical creatures. Many times, kids fear things because they have overheard parents or adults say things like, "I hated math too, Sue, so don't feel so bad," or "I know. Fractions are the pits, Johnny." Rather than instill fear of the unknown, you as parents, need to instill joyous expectancy.
- This is One Tough World in Which to Raise Kids
[Home-and-Family:Parenting] The world of today is not a favorable one in which to raise kids. With morals falling to unprecedented lows and both parents working round the clock to maintain just the barest essentials of a lifestyle, kids are being left exposed to a world of internet porn, harsh and strife-inducing music, and a whole array of other toxic mental poison. Technology, while blessing us with comforts and conveniences that would have been unimaginable just a generation ago, has spawned economic hardship for parents trying to give their kids the latest high-tech fodder. Basically, what this new world paradigm has done is place unprecedented pressure on parents trying to raise healthy, responsible children.
- Why Study Math? - The Odds of Becoming Rich
[Reference-and-Education] So you think you can strike it rich with the lotto? Well, maybe you can, but I have to tell you that the odds are not that good. In fact, according to mathematics your odds of winning are essentially nil. Understanding math and probability will allow you to calculate your probability of striking it rich in any given year, but then again maybe this knowledge might depress you somewhat- for the chance of you getting that big check is actually a lot less than your chance of being struck by lightning.
- Math Can Be Strange but Quantum Physics is Even Stranger - Part II
[Reference-and-Education] "A whiff of a quiff is enough of a sniff to cause quite a tiff though quixotic the riff."
— Author known but intentionally not revealed
At the subatomic level some really strange things start to happen: new worlds of thought and curiosity are opened up, the improbable becomes highly probable, and the usual becomes quite the unusual. In fact, it is at this level that man starts to contemplate the reality of his own existence since quantum physics dares one to ask the question, "Is reality real, or just a figment of my imagination?"
- Recipe for Success in Math
[Reference-and-Education] Obviously, math is important in the real world. What is amazing to me is how many people get by without an even basic understanding of this most helpful subject. True, most people do not need to understand what a topological space is, or why certain functions are continuous and others not, or what the relevance of this idea is anyway; but knowing how to be quick with numbers, and understanding the nature of fractions and how they are used in the real world, as well as knowing the basics of geometry, are an absolute necessity to do better than average in this difficult world we live in.
- Math Can Be Strange but Quantum Physics is Even Stranger - Part I
[Reference-and-Education] Indeed math can be strange. Especially when one delves into the upper echelons of this most mystifying discipline: multidimensional spaces, transfinite numbers, non-Euclidean geometries—you name it. But when you start reading about quantum physics and all the strange things that happen at the most microscopic of microscopic levels, then you really start to realize that math is not all that strange.
- Fractions- Why Are They So Hard?
[Reference-and-Education] Not even signed numbers cause as many problems as those two-headed monsters called fractions. But why so much trouble? Maybe because fractions have a dual nature, that is, they consist of the numerator and denominator, and most of us are poor at multitasking. But did you know that once you master fractions, you learn to handle multiple tasks as well? This is one of the benefits of mastering these pesky little creatures.
- James Bond and Math- Two of a Kind
[Arts-and-Entertainment:Movies-TV] Anyone who has watched any of the classic James Bond movies, particularly the earlier ones like "Diamonds are Forever" with Sean Connery, and "Live and Let Die" with Roger Moore, knows that the man with the plan, namely Agent 007, was beyond cool. He could woo the beauties like no other, defend himself in any of a dozen ways, get out of the tightest spots imaginable, and adapt comfortably to any situation, whether this find him trapped in a sewer with rats, or cavorting in a tuxedo while attending the latest royal function. With all his debonair mannerisms and sophisticated abilities, do you really think James Bond was a pushover in math? I highly doubt it.
- What's Wrong with Education in America?
[Reference-and-Education] Why is education so bad in America compared to other countries? I'm sick and tired of reading and hearing about all the bad things in the American educational system. As a former teacher of both college and high school mathematics, I find my insides turning every time I read a report on how we are failing our children. But are we failing, or are there other factors which need to be addressed? Let's take a look at these.
- Why Study Calculus? - How About Cube Roots Without a Calculator!
[Reference-and-Education] If you thought that the only purpose of calculus was to confuse you, then think again. Continuing with my Why Study Calculus? series, I discuss yet another application of this branch of mathematics to numbers. Numbers and the operations performed on them are the linchpins to mathematics, and all higher branches are one way or another intimately linked to their inherent properties. One nice application of the Calculus to numbers is the approximation of cube roots. What is enticing is that this technique can be done without a calculator and without even a knowledge of the underlying theory.
- The Secret to Life - It's All in a Word
[Self-Improvement:Spirituality] People are always looking hard to find the answers to things that are quite simple. Take life for example. How many times have you heard someone ask, "What's the secret to life?" You sit there scratching your head saying to yourself that if you knew the answer, you wouldn’t be where you were today. However, you and I do know the answer to this question- we just might not have been exposed to its effects enough, and for this very reason, are not able to experience the power of its knowledge. The secret, you see, all lies in a word.
- Do Your Kids a Favor - Take Away the Calculator
[Reference-and-Education] The kids of today are so different from those of only a generation ago. Heck. I'm quite computer literate and am pretty good with electronic gadgets, but I can't even place a close second to my two kids' ability with video games and other technological toys. Yet this ability with gadgets has placed our children at a disadvantage as well. You see. They have come to lean too heavily on the electronic calculator, and this dependency has severely weakened their ability in math.
- Mathematics and the KISS Principle
[Reference-and-Education] Keep it simple, stupid! That phrase resounds in your brain while you contemplate how it could ever be applied to your current course in mathematics. You remember hearing that if you kept things simple, then things would keep you. Yet you're mired in difficulty, you need to get a decent grade in your current course, and all you can think of is failure, failure, failure. What do you do?
- Why Study Math? Prime Numbers
[Reference-and-Education] Remember when you were back in grade school and your teacher was going over basic arithmetic and numbers? You learned basic facts about division, as for example, how to know whether a given number is divisible by 2 or 3. You also learned about composite numbers and prime numbers. You sat there scratching your head wondering how in God's name such a thing as a prime number would ever have any use other than to give young children homework headaches. But then again God has a funny way of letting each one of his creations participate in the grand scheme of things - yes even creations like numbers.
- Hey, Who Said You Couldn't Do Math? - It's All in Your Head
[Reference-and-Education] So you think you can't do math, huh? Well, what if I told you that without even an algebra background I could teach you some calculus right here and now? You don't believe me. I thought so. This unbelief proves how programmed you've been from early on to reject mathematical teachings. Whoever laid this negativity on you really did a number on you. Well, let’s get rid of that negative programming and feed you some really positive stuff.
- Hey Kids - It's Cool to be Square
[Self-Improvement:Leadership] This article goes out to this generation of teenagers who think that being cool means smoking dope, hanging out with their drug-taking friends, having promiscuous sex, and being defiant to authority figures like teachers, police, and yes-parents. This behavior is not cool but rather dopey. You see, before long you will be entering the real world, and the real world does not take particularly well to defiance or irresponsible attitudes. Enter the world expecting it to give you freebies just because you deserve them and you will soon be wishing you listened to your parents and acted more square than cool.
- Concepts In Infinity – Some Ideas To Ponder
[Reference-and-Education] Could God really be lurking within the extraordinary realm of mathematics? Could the language of God be closely connected to the language of mathematics? How could a set of numbers be connected to the infinite mind of God and the infinite expanse of the universe? Well read on to get a fascinating glimpse into this most extraordinary idea.
- Take a Bow Stephon Marbury - Boo Michael Jordan
[Business:Marketing] When I watched John Stossell's show on the comparison between Michael Jordan's Air Jordan sneaker line and Stephon Marbury's Starbury line, I quickly realized that greed in America is becoming more and more the rule rather than the exception. To wit, the shoe experts cut open the two brands of sneakers and found that there were no essential differences -only price. That Marbury can sell his shoes for $15 while Jordan sells his for up to $175-200 per pair only shows that marketing hype is big business and that some people are just never satisfied in ripping off the public.
- Reading and Reviewing Articles - Be Fair, Not Square
[Writing-and-Speaking:Writing-Articles] For those of you who have discovered article writing as a way to get worldwide internet exposure, take a bow. Welcome to the international brotherhood of article writers. As part of this brotherhood, you should be aware of some article etiquette, particularly as pertains to supporting and encouraging your article brothers. One of these manners of etiquette has to do with rating articles.
- If You're Selfish, Teaching's Not for You
[Business:Careers-Employment] Thinking of entering the teaching profession? Maybe you're even thinking of teaching a subject like mathematics. What a crazy thought! Why would you want to do such a thing? I mean, I can come up with at least a hundred other ways of frustrating the heck out of yourself. All joking aside, teaching has to be the most noble profession on earth, but one that should not be entered into on a wing and a prayer, nor after only perfunctory consideration. And if you are selfish, then teaching is definitely not for you.
- Taking Back Our Youth - A Plea for Unity
[Home-and-Family:Parenting] So you're tired too of dealing with your teenage son or daughter? You mean you're walking on eggshells when he or she is home? Can't get them out of bed in the morning? Having trouble getting them to follow any rules? Well, welcome to child rearing in the rip-roaring new millennium.
- Learn Math Through Poetry
[Reference-and-Education] Since mathematics as a whole is a difficult subject to learn, maybe different approaches are needed in the teaching of this discipline. Certainly the hands-on approach gives students a tactile perspective to the inner workings of this subject, while the real-life applications approach lets students see and understand how mathematics is used in the real world and in different worldly settings. Could poetry be another approach through which to teach and learn this most fascinating subject?
- Eulogy on the Sonnet
[Writing-and-Speaking:Writing] There is just something simply elegant about packing a ton of meaning into a fourteen line poem, which we know as the sonnet. I came to write sonnets as a result of having been asked by a student, whom I was tutoring over the internet via email, to help her with an English assignment. This task involved writing a sonnet. Having been a big fan of the Sonnets of William Shakespeare (having memorized at one time at least twenty-five or so, and having written a short book on the subject), I delighted in the task. The result was that I became an avid writer of this famous English poem.
- Teach Your Kids Algebra: The Quadratic Formula
[Reference-and-Education] When I first saw the quadratic formula, I was amazed that there existed such a thing no less a way to derive this elegant formula. For those who remember, this formula gives a sure-fire way of getting the solution to those things we call quadratic, or second-degree equations, in mathematics. For many students, this formula is a nightmare of grand proportions and its mastery seems no more probable than striking it rich with the lottery. However, with some novel techniques and some different approaches, the mastery of this formula—which provides a linchpin to understanding algebra on a deeper level—becomes a walk in the park.
- Rap Music - Good for our Children's Ears?
[Arts-and-Entertainment:Music] So we all know the rap music industry is big business. How big? Assuredly in the billions of dollars. But is this rap music—and more specifically the genre referred to as gangsta rap—good for our children's ears and moreover society? Common sense would dictate that the last question is quite a rhetorical one.
- Einstein's Number Trick: Fun for All
[Reference-and-Education] When we attach the name Einstein to a number trick, however, the idea takes on an entirely different dimension, both literally and figuratively. If you are interested in some fun with numbers, try out the trick below on some friends and family, and by all means teach it to your kids, if you have any.
- Teenage Problems and Math - Could There Be a Connection?
[Reference-and-Education] Children who are difficult to manage are often poor problem solvers. Any parent who is experiencing trouble raising their teenage son or daughter knows how vexing a problem this can be. My wife and I experienced this firsthand and I can honestly tell you that the trials we went through were nothing short of nightmarish. After purchasing a specialized program to teach us how to deal with this problem, we learned that children who are behavior problems are often poor problem solvers. It was then that I saw a revelatory connection.
- Why Study Calculus? How About Square Roots With No Calculator?
[Reference-and-Education] To continue with my Why Study Calculus? series, I discuss here some interesting applications of this branch of mathematics to numbers. Numbers and the operations on them are the key to mathematics, and all higher branches are one way or another intimately linked to their inherent properties. One nice application of the Calculus to numbers is the approximation of square roots. What is more, this technique can be done without a calculator and without even a knowledge of the underlying theory.
- Why Study Calculus? - Area of Irregular Shapes
[Reference-and-Education] You know I thank God that I was given the ability to communicate math to the masses. I guess this talent comes from my struggles with this subject early on. My ability to convey the guts of this subject derives from my belief that if I can understand it, anyone can. Such is the case with calculus. Read on as I show you how this subject allows us to calculate the exact area of even bizarrely shaped objects.
- Don't Mind Me - I'm Just a Mathematician
[Self-Improvement] Look. Just because a person is a mathematician and loves numbers and that sort of thing, doesn't mean this person is an absolute weirdo. You know, if you meet me in person, I don't really look like a mathematician, or someone who spends time reading about things like topological spaces or the construction of real numbers using Cauchy Sequences. In fact, I think I'm downright cool because I like this stuff, and this attitude is what enables me to bring this subject to others and make it understandable to the math haters.
- What Your Kids Need to Know to Excel in Math
[Reference-and-Education] Do you really want to get your kids off to a fast start in math? Then they need to know some basic facts. Teach kids their addition and subtraction facts as early on as possible. Once conquered, move on to multiplication facts. Finally, start plodding into the territory of division. With the four pillars of arithmetic conquered, your kids will be on the fast track to academic success.
- The Best Christmas Gift I Ever Got
[Self-Improvement:Spirituality] There are times in one’s life when something so miraculous happens that it defies ordinary explanation. We all hear of amazing stories—of miraculous recoveries from disease or illness, of daring escapes, of angelic interventions—but when it happens to you, you don’t know quite how to explain it other than to say thank you God, and praise be Yours. Something like this happened to me today, and I describe it as the best Christmas gift I ever got. Here I relate the details.
- Using Math to Keep From Getting the Common Cold - Or Worse!
[Reference-and-Education] We all know how annoying and vexing the common cold virus can be, particularly during the winter season. Nobody likes that runny nose or that constant urge to sneeze; nor is the coughing, headache, or scratchy throat anything to write home about. To avoid catching the common cold, we know that we should wash our hands often and keep from being breathed or sneezed on by those already infected. Yet despite all our efforts, we still seem to get that yearly cold. Maybe mathematics has some clues as to how we might lessen our chance to pick up that awful cold.
- How an Article on Math Got Me a Spot on Fox TV
[Writing-and-Speaking:Writing-Articles] So you love to write and you found out about submitting articles on the worldwide web. You ask yourself whether you can actually get good exposure from spending time writing articles and whether it’s worth the effort. After all, like me, you’re a nobody from nowhere. But then again, at one time so were all the celebrities and people in the current media. Well, I started writing articles a little less than a year ago, and when I started, I asked the same questions. Now that the Fox TV interview has aired on television and on their website, I am thoroughly convinced that, yes, article writing is worth the effort. Read on.
- Teaching Algebra: Slay the Demons First The Rest Is Easy
[Reference-and-Education] Labor Day is fast approaching and you can almost smell the students at the front door of your classroom. Another year and another sixty or so Algebra I students to grapple with. And although the first few weeks might go fine, you know that as you hit the third chapter or so of the text, the kids will start having problems. You dread having to explain things over and over again, and you loathe grading those awful tests. You just can’t understand how the students don’t get it. To you it’s all trivial but to them it's relativistic mechanics. Ponder this situation as you may, what you might not have realized is that if you slay the demons first, the rest is - well easy.
- Effective High School Math Teaching: A Recipe for Success
[Reference-and-Education] Why is math so hard to teach and why are there so few good math teachers? Whether you are a student, parent, or yes—even a math teacher—you know how true this question is. Effective math teaching requires more than just a good handle on the subject. A great high school math teacher must be a great salesperson; moreover, effective teaching—period—requires that the teacher be a better salesperson than the students. For if you can sell the students your bag of goods successfully every day, then your knowledge of the subject becomes a secondary attribute. Additionally, if you manifest a genuine concern for the individuals that you teach, mix this with a little humor, present the material with a commanding knowledge, and show enthusiasm for what you are selling, then the victory will be easily at hand.
- Why Study Math? Fractals
[Reference-and-Education] Mathematics has a way of taking us by the hand and not just leading us down the path of reason, as Pythagoras once said, but sometimes down the path of insanity. With all the beautiful truths that math can show us, there are also inherent contradictions of nature that this field forces upon our senses. Such seeming impossibilities are found within the world of fractals, those weird yet curious geometric objects that have caused us to look at nature in a whole new way. From the surface of a mountain to the head of a broccoli, fractals are being used to explain things that we normally take for granted.
- Math Is Hard - But Then Again So Is Life
[Reference-and-Education] When I contemplate the title of this article, I enter a reverie which catapults me back twenty-five years to my college days. Back then, I learned how hard mathematics was. Often I felt inferior to tackle such a difficult subject with my limited brain capacity. Little did I know then that in retrospect I would come to understand that indeed math is hard, but that life too is just as challenging.
- Why Kick Yourself When the World is Already Doing a Good Job of It?
[Self-Improvement:Positive-Attitude] Nothing smarts so much as when the world gives you a good butt-kicking. Nobody—not even the rich and famous—are immune to such occasional whippings. But the rich, famous, and highly successful have their riches, fame, and financial success to lean back upon. What do the regular average Joe’s and Jane’s have to lean on when the cold world turns its ugly head and starts its unrelenting chase?
- Article Writing - Your Key to Good Exposure
[Writing-and-Speaking:Writing-Articles] Writing has always been a favorite pastime of mine. When I discovered article writing a year ago, the means for expressing myself as well as the ability to share my knowledge with others became possible. This open forum has created a dialogue with my readers, who although unknown to me, create the necessary feedback that drives me to write even more. Moreover, well written and interesting articles can pave the way for much exposure—even to the extent of news related stories and television interviews.
- Why Study Math - Probability and the Birthday Paradox
[Reference-and-Education] When I decided to become a mathematics major in college, I knew that in order to complete this degree, two of the required courses—besides advanced calculus—were Probability Theory and Math 52, which was statistics. Although probability was a course I was looking forward to, given my penchant for numbers and games of chance, I quickly learned that this theoretical math course was no walk in the park. This notwithstanding, it was in this course that I learned about the birthday paradox and the mathematics behind it. Yes, in a room of about twenty-five people the odds that at least two share a common birthday are better than 50-50. Read on and see why.
- Why Study Calculus - The Limit
[Reference-and-Education] Calculus does have its limits. Indeed. In order to understand the pun of the first sentence, you need to know that calculus has two key branches: differential and integral. Although the concept of limit belongs to both branches and is an essential component to the understanding and mastery of this kind of math, differential calculus gets its name from the derivative; and such a creature depends entirely on the concept of limit. In fact, the derivative is nothing more than a special kind of limit.
- You're Kid's A Genius! - The Illusion Has Become Real
[Self-Improvement:Attraction] There’s an old joke about two schoolboys that basically goes as follows: Johnny, one of the boys would go off to school every morning, and as he left his mother would yell, “Johnny, don’t forget your lunch!” The other boy, Steven, would go off, and as he did, his mother would yell, “Steven, don’t forget your books!” Johnny grew up to be a successful restaurateur and Steven a world-renowned brain surgeon.
- A Poem a Day Keeps the Heartache Away
[Self-Improvement:Spirituality] In this complex world of technological gadgetry, we run at a pace which would make our ancestors blush at the thought. Faxes are not even fast enough as we have email which is instantaneous. And no matter that you are not at your computer because many cell phones deliver email in a snap. The latest news from abroad—good or bad—the latest stock quotes to brighten or stress your day—it's all there in a digitally quick transmission of electrons. Is it any wonder that we have little or no time for self-reflection, for a quiet moment far from the maddening crowd?
- Teach Your Kids Arithmetic - Subtraction Shortcuts
[Reference-and-Education:Home-Schooling] As students, we become comfortable with what we learn first. Of the four arithmetic operations of addition, subtraction, multiplication, and division, we learn to add first and for this reason are most comfortable with addition. If we apply the principle of thinking in terms of what we are most comfortable with, then subtraction need not be a difficult operation to master. Consequently, by applying addition principles to subtraction, we find our shortcut to mastery of this operation.
- Algebracadabra - Math Shortcuts to Algebra Mastery
[Reference-and-Education] Probably the most important fundamental branch of mathematics is algebra. No matter what anyone tells you folks, if your kid is not good at algebra, there is no shot that he will excel in any of the higher branches. In fact, the famous calculus is really a form of "glorified" algebra and this is what I used to tell my high school students all the time. Therefore, if you want your kids to have a chance to study and enter the beautifully intellectual realm of the calculus, then be sure that they have the tools to master algebra.
- Teach Your Kids Arithmetic - Division Shortcuts
[Reference-and-Education:Science] The famous Greek mathematician Pythagoras (you know the one with that theorem) said, "Numbers have a way of taking you by the hand and leading you down the path of reason." What Pythagoras was getting at, I think, is that numbers - by their very nature - permit us to do things which enable an understanding of the very universe and its intricate laws. Numbers have their roots in arithmetic, and a mastery of this field, particularly the operations of addition, subtraction, multiplication, and - yes that monster operation of division - will certainly pave a smooth road down that path of reason.
- Mastering Arithmetic and Singapore - What’s the Connection?
[Reference-and-Education] The name Singapore derives from two Malay words meaning “lion city.” So what’s the connection between this small South-East Asian country of four million and arithmetic mastery? Well for one, the Singaporean mentality toward arithmetic mastery as the stepping stone to higher mathematics is as well ingrained in their culture as apple pie and baseball is in ours. Indeed their lion-like ferocity toward taking no prisoners in insuring that their children master the mathematical basics of arithmetic—to wit, multiplication, division, addition, and subtraction—is the main reason that their country serves as a model in educational excellence, particularly in the mathematical and scientific fields.
- HSPA Mathematics New Jersey Test Preparation
[Reference-and-Education] The New Jersey HSPA (High School Proficiency Assessment) Test is one which all juniors in New Jersey high schools must take and pass in order to receive their diplomas. For many, this test presents a challenge as it consists of two sections, one in English, and one in math. The English section requires that students demonstrate competency in English, both from a written and comprehension perspective; and the math section requires students to demonstrate competency in four areas in high school mathematics: number sense, concepts, and applications; spatial sense and geometry; data analysis, probability, statistics, and discrete mathematics; and patterns, functions, and algebra.
- The Seven Follies of the Common Man - Part I
[Self-Improvement] What sets the exceptional man apart from the common man is the way in which he approaches most day-to-day dealings. The exceptional man knows that no good deed goes unnoticed nor does it go unreturned. Just as night must follow day, good must follow good, truth must follow truth, and justice must follow justice. This is something that the common man simply does not understand for he is plagued by the seven follies. What are the seven follies and why the to-do about this concept?
- The Seven Follies of the Common Man - Part II
[Self-Improvement] In Part II of this article, I discuss the other three follies of the common man: hate, spite, and unforgiveness. Clearly, these are three negative qualities, the first two being very strong negative emotions, and the last being a cancer-causing bitterness-arousing trait. These follies wreak havoc on a man’s emotional state of being and cause all kinds of disturbing conditions even to the point of making man sick. Let’s discuss how we can avoid the pitfalls into which these three follies plunge us and recognize ways to rid ourselves of these onerous states.
- College Essay Preparation
[Reference-and-Education:College-University] Submitting a good college essay is another aspect that has to be considered by the high school student who wishes to attend a competitive school. This essay, together with the SAT (see my article on SAT Test Preparation), are two key aspects that must be satisfactorily completed by the college-bound student. Sometimes the college essay is what makes or breaks a student’s chances of getting into the school of his or her choice.
- SAT Test Preparation
[Reference-and-Education:College-University] For many juniors in high school, the SAT (Scholastic Aptitude Test) looms as a big ugly monster on the horizon. Indeed for both parents and students, the anticipation of taking this test creates all kinds of unwelcome anxiety. The stress becomes enhanced for the competitive college-bound individual who wants to get into a better-than-average school. In order to achieve a respectable score on the SAT and to ward off excessive amounts of stress, students should give adequate time to prepare for this examination. For those parents who can afford it, private tutoring and specialized schools are also available.
- Effective E-Mail Math Tutoring
[Reference-and-Education:Online-Education] When people think of additional school help for their child who is struggling in math, they usually think of one-on-one private tutoring. Private tutoring is a great way to get help for your struggling child. As mentioned in my article on effective math tutoring, the knowledge that a tutor brings to the table is not so important as his ability to relate well to your child and to identify with their source of difficulty. Even though private tutoring is the way parents think they need to go, there are alternatives such as email tutoring that can be a welcome help to your child.
- Problem of the Week - Some Good Old Mind Stimulation
[Reference-and-Education] Just as physical exercise is needed for the body, mental exercise is needed for the mind. In fact, research has shown that giving the mind a good workout regularly not only keeps those neuronal passageways clear and efficient but also mitigates against the age-induced problems that come with senescence. For this reason, a crossword or two, perhaps some sudoku—even some plain old number games—will do both you and your mind a lot of good. The feature on my website called Problem of the Week will help you achieve this mind-stimulating objective.
- Effective Math Tutoring
[Reference-and-Education:Home-Schooling] People may think that the key to effective math tutoring, or tutoring in any area for that matter, is contingent upon the knowledge that the tutor brings to the table. While knowledge of one's field is certainly important if a tutor is going to be effective, more important is the tutor's ability to relate to your child and give him or her the necessary confidence to succeed in the math subject at hand. During my many years of math tutoring, students would come to know that I knew my field well, but more importantly they came to know that I could relate to them on a deeply personal level. Once this aspect of the tutor-student relationship is established, tutoring becomes markedly more effective.
- Beside the Still Waters
[Arts-and-Entertainment:Poetry] Sometimes a poem can move us to such soothing emotions that we get a sense of calm and healing just from reading through to the end. Beside the Still Waters paints a picture of such beautiful imagery and halcyonic scenery that we come away with a fresh perspective on life, and perhaps a new perspective on faith. Read and enjoy.
- I Hate Fractions
[Reference-and-Education:Home-Schooling] Fractions are the pits. You know you can’t just add or subtract them even though multiplying and dividing them is not too bad. But since addition is the most popular arithmetic operation, that’s where the darn problem is. I mean those pesky denominators always get in the way. Yet fractions appear everywhere you look: look at the price of gas, which is hovering about $3.00 per gallon and you see something like "Unleaded Regular - $2.79 9/10"; or take a look at the unit prices in supermarkets and you might see something like 33 ½ cents per pound, or 16 1/3 cents per ounce. Let’s face it, you’re not escaping these little monsters so you better just get used to them.
- Be Smart - Love Your Neighbor
[Self-Improvement:Spirituality] You know it troubles me more and more each day as I watch what is going on around us in this world. It seems today more than ever that individuals are so focused on themselves, exhibiting a level of self-centered, egocentric, and selfish tendencies that are unprecedented. Caring about one another or showing empathy toward others does not even factor into any equation whatsoever. In the New Testament book of Hebrews, Paul talks about letting brotherly love continue; yet today more and more people are concerned about letting their selfish ways perpetuate. This is most evident in the youth of today. This condition is sad, as we prosper or stagnate in proportion to the support and help we lend to each other as human beings.
- Death Knows No Bounds
[Self-Improvement:Grief-Loss] Having just returned from the wake of a friend whose sister was killed in an apparent murder-suicide, I found myself wondering about the fragility of life and how close we all are to the portal of death. This too was the second time in a month that I was in the same funeral parlor room, the first time to pay my respects to a beautiful young woman of forty-four years who succumbed to Lou Gherig's disease, whose middle son was good friends with my younger son; and now to pay my respects to the two brothers of this thirty-two year old beautiful woman who was murdered by her husband. What made these two wakes particularly tragic was that each woman left behind young children, each was both beautiful and young, and each had great families and very successful lives from a financial perspective.
- Teach Your Kids Arithmetic - The Magic of "One" Numbers - Part II
[Reference-and-Education:Home-Schooling] As a follow up to my article "The Magic of One Numbers Part I" I now continue with Part II in this fascinating series. For those who have not read the first article, please do so now so that you can better understand this one. Here I will show you a method to perform the multiplication of any two "one" numbers regardless of size. The result of such multiplication—once this method is studied and learned—can be obtained effortlessly and usually within seconds. So let’s get started.
- Teach Your Kids Arithmetic - The Magic of "One" Numbers - Part I
[Reference-and-Education:Home-Schooling] Do you know that numbers are the key to life? Indeed numbers form the foundations of mathematics from number theory all the way up to partial differential equations. Without these curious creatures, we could not calculate, estimate, or compute (as in computer); nor could we transact any of the business that occurs daily throughout the known world. Yet most people find these most interesting entities just a bothersome part of life. Why should this be so? Well maybe a person’s ambivalence towards numbers derives from childhood frustrations experienced when struggling to learn the basics of arithmetic and the rote calculations associated with this discipline.
- You Must Excel in Math
[Kids-and-Teens] You must excel in math for many reasons. Math by its very nature is a rigorous subject which conditions the mind to work more efficiently than it otherwise would. One of the reasons I teach my short-cut arithmetic techniques is so that people who learn them can exercise their brains regularly. Indeed such exercise not only stimulates the mind, but also helps keep your brain younger and less prone to degenerative diseases and decreased cognitive functioning. And there is no better brain stimulation than that obtained while you navigate within the mathematical disciplines, trying to work and solve problems of myriad levels of difficulty.
- Aim High, Just be Willing to Work for It
[Self-Improvement:Motivation] "Aim High! There is little virtue in easy victory."
—Sir Edmund Hillary, who with Sherpa guide Tenzing Norgay, was the first man to successfully summit Mount Everest.
Think of the effort that Sir Edmund Hillary must have put in to mount the 29,035 feet of the Himalayan giant Mount Everest. And we think that internet marketing is hard! Yet in spite of the difficulty that is inherent in mountain climbing expeditions, there are challenges in climbing the oft reputed internet peaks that dot the cyperspace landscape. These are obstacles that any person new to this arena faces. Web site optimization, traffic regulation, search engine submission—where does it end? Each of these mountain peaks has sub-peaks, and every time we think we have reached the top, we see that—as the famous poet Alexander Pope said — "Alps on Alps arise."
- Teach Your Kids Arithmetic - The Teenage Number Trick
[Reference-and-Education:Home-Schooling] So you think you can’t do math in your head, huh? Well, it all depends on how you do such math. After all, if given the right tools to do a job, then the job comes out right often enough. So why fret over the small stuff? Too often mathematics is made out to be some mysterious subject, only to be mastered by an esoteric group of like-minded nerds who co-habitate in some forsaken land. Well, that’s not the case and one of the things I’m fond of doing is debunking this oft-held yet misguided notion.
- Beware the Internet Shark - Hypocrites
[Internet-and-Businesses-Online] If there is one thing I cannot stand more than anything else, it has to be the internet shark-hypocrite. What do I mean by this? An internet shark-hypocrite is one who goes around parading like your best friend in cyberspace, one who can help you achieve whatever your heart desires, when in fact he is really a lying shark ready to pounce on you at the first scent of blood. In the days since the internet boom, shark-hypocrites have multiplied to the point at which a person in search of some help on the internet, particularly as concerns making some extra money, cannot avoid being attacked by these omnipresent and conniving beasts. Despite their growing numbers, I will not cease to expose them at every turn, trying to educate readers of my articles so that they do not become a sumptuous meal for these lurid creatures.
- Teaching Mathematics: Alternative Strategies That Can Be Taken to the Bank
[Reference-and-Education] As a former teacher of high school mathematics, I understand the day-to-day frustrations that any teacher might experience, particularly when trying to teach a subject like mathematics. The first day of class was always interesting. As teacher, I felt like the enemy who was bringing messages of death and despair to the students. I could see in many of their faces how dreaded a subject this truly was. But I would win them over. Yes, one by one I would quench their fear and instill new hope.
- Teach Your Kids Arithmetic - Arithmetic and Fraction Mastery
[Reference-and-Education] You know it’s true. If you want your children to master mathematics, you need to give them certain tools so that they can whip the heck out of this difficult subject. One of those tools is a mastery of arithmetic. Another is a mastery of fractions. These two together will give your children a formidable arsenal against this notorious subject.
- Counting All the Way to the Bank
[Internet-and-Businesses-Online] You know it's funny. I'm making so much money online that I can't believe it's true. These internet gurus out there who sell all those money making programs are right. I'm about to quit my job because of them and spend most of my time at the gym and on the beach this summer. I might even cruise down to some of the islands—maybe even take a stroll through Hawaii. My Paypal account is about ready to explode. What a great life!
- Internet Hype - Do Leave Home Without It!
[Internet-and-Businesses-Online:Internet-Marketing] All right. I’m sick and tired of all the hype on the internet. And I can’t believe people actually fall for this stuff. You know, the promises of six-figure incomes—not yearly—but monthly; the promises to help you leave your day job within three months; the promises to give you the knowledge to work three hours per day or less and spend the rest of the time on the golf course or at the gym. Come on. As John Stossel says, "Give me a break!"
- Teach Your Kids Arithmetic - Calculations with Percents
[Reference-and-Education] How important on a scale of 1 to 10 would you say knowing how to do basic percents was? Personally, I cannot think of a more important basic math function than this. Yet most people struggle with the very basics of percent calculations. This should not be the case. My aim in writing Arithmetic Magic was to show people that they can do basic arithmetic, and this once realized would empower them to study math at a higher level and become more interested in this most precious discipline.
- Math Geeks are Cool
[Reference-and-Education] Why is it that math geeks are considered squares? That is, why is the straight-A math student considered Mr. Un-popular in school? It’s funny how twisted things are in life. The cool kids in school are the ones smoking pot and cigarettes, perhaps taking other illegal substances, having sex with other students, and getting into at least one fight per quarter. Meanwhile, the straight-A kids are considered geeks, even though they are the ones that will build the country, write the future laws, and find the cures for the most vicious diseases that affect us all today.
- Math and Poetry
[Reference-and-Education] Math rules, and everything else drools. Well maybe not everything, but the truth is that math really is the king of subjects to study. For ultimately every subject in school—indeed everything—revolves around math. Even subjects that you would never think. Like English, for example. How so? you say.
- Why Study Math? - The Hyperbola
[Reference-and-Education] As we continue the “Why Study Math” series of articles, here we look at the conic section called the hyperbola. The hyperbola is obtained by intersecting the double-napped cone (see the other articles in this series on this point) with a plane so that both parts of the cone are cut. Those familiar with the parabola might note that this curve almost looks like two parabolas pasted back to back with a space in between them. Mathematically, the hyperbola is not a parabola, although these two conic sections have a similar outward appearance.
- Why Study Math? The Parabola
[Reference-and-Education] As we continue the "Why Study Math" series of articles, here we look at the conic section called the parabola. The parabola is obtained by slicing a nap of the cone (see the other articles in this series on this point) with a plane parallel to one of the generators of the cone.
- Why Study Math? The Ellipse
[Reference-and-Education] Why study math? You're kidding right? The next time you hop in that new spit-shined Mercedes of yours and start to rev the engine, remember that had it not been for the study and application of the ellipse, you might be picking up your sexy date in a horse and buggy. Read on.
- Arithmetic Magic - The Introduction
[Reference-and-Education] Read the introduction to Arithmetic Magic and learn how you can finally develop confidence in math. It all starts with numbers, for once we can work with them, the rest is easy. Read on.
- Teach Your Kids Arithmetic - Fractions, Percents, and Decimals
[Reference-and-Education:Home-Schooling] Admittedly fractions are trouble for most students. In my previous article I talked about why this is so. Percents and decimals too present their share of problems to young students-adults as well. There is an interesting connection between these three mathematical entities and here it is: fractions, percents, and decimals are variations of one and the same thing.
- But I Want to be Popular Too
[Self-Improvement:Attraction] Let’s face it. We all want to be popular. Popular with friends, relatives (well, maybe not relatives—just kidding), coworkers, bosses, and so on. Popularity is associated with fun times, success, prosperity, and a whole array of other positive thoughts and emotions.
- Teach Your Kids Arithmetic - Fractions, Those Devils!
[Reference-and-Education] Fractions. Ugh! I could just hear the squeals coming from my students any time we entered the realm of these nasty little demons. Anytime we embarked on an area of mathematics that would require heavy fraction work, students would act as though we were entering Hades after an arduous crossing of the river Acheron, led by the fearless ferry-man Charon and his three-headed dog Cerberus. Ouch! It was that bad.
- Why Study Math? - The Circle
[Reference-and-Education] Analytic Geometry is a branch of mathematics that treats the relation of algebraic functions and their respective graphs, or pictures that can be drawn from these functions. Students are first introduced to analytic geometry in Algebra II courses, and delve further into its study in both pre-calculus and calculus courses. Essentially, this branch of mathematics combines geometry and algebra to show what certain mathematical relationships, called functions, look like in the real world.
- Why Study Math? - The Polyhedron
[Reference-and-Education] This article will launch my new series in the Why Study Math? category. This will be the start of a fascinating series which show that mathematics is more than just a pain in the neck; indeed these essays will permit a fascinating peek into the world of this curiously strange discipline. We start in the land of geometry, where shapes and figures and their many properties drive students to the breaking point of insanity. Each article will feature a specific aspect of a particular branch of mathematics, such as algebra, trigonometry, and calculus; and each will endeavor to shed some light on how these fields are used in the real world. So come on board and enjoy the ride.
- Much Ado About Oprah's Book Club
[Book-Reviews:Lifestyle] In Amazon’s Significant Seven interview with Jim Frey, the controversial author of the Oprah Book Club selection, "A Million Little Pieces," he was asked: "If you could have one superpower what would it be?" Anyone want to guess what that superpower might be?
- Keep those Modifiers from Dangling, George!
[Writing-and-Speaking:Writing] If you want to write well, one of the stylistic elements that you need to pay heed are those nasty dangling modifiers, whether in participial, gerund, or phrasal form. Although sometimes insidious to spot, these grammatical faux-pas will tinge your writing and confuse your readers' train of thought. Much like a poorly segued musical transition, dangling modifiers impinge somewhat strangely on the ear and often lend unintended yet grotesque humor to your writing in general.
- 20/20 Speaks Out on Education in America
[Reference-and-Education] The other night I was watching an episode of the show 20/20, in which John Stossell was exposing the dreadful situation of education in the American schools. In this episode, the host made a comparison between our schools and those in Belgium. For this comparison a test was administered to both American and Belgian students of the same age. To wit, the Belgian students clocked the Americans on this test. What stung even more for the American cause was that the American kids were from a rather decent school. Wow! How dreadful. Yet this state within American schools is something I witnessed firsthand.
- Teach Your Kids Arithmetic - The Quick-Add - Part II
[Reference-and-Education] Children need arithmetic, particularly in the early years of their education. When they start to stumble in this most important discipline, their attitudes quickly turn rebarbative towards mathematics in general, and their future success in this area is seriously—if not permanently—impaired. With some clever tools, however, this threat is obviated; children are then liberated to succeed in mathematics and prosper in their academics. Here in Part II of this series, we show how to work the Quick-Add.
- Attack the Bible - Shame on You!
[News-and-Society:Religion] Are attacks on the Bible really justified. Children believe in Santa Claus, the Tooth Fairy, and the Easter Bunny up till a certain age. Do we dare attack these cherished beliefs because we know otherwise? We uphold these out of love for our children, our grandchildren, our nephews and nieces. So dare men risk attacking something that they cannot prove false? This is the epitome of both arrogance and foolishness.
- Taking Back Sunday
[Home-and-Family:Parenting] As parents, teachers---human beings---we need to take a stand against the steadily eroding social values in our youth. How do you think the Puritans who came over on the Mayflower would react if they could get a sneak preview of the way adolescents behave today? Yes, there are good teens; let's bring more over to this side.
- Nice Guys Finish Last - Or Do They?
[Self-Improvement:Spirituality] If you are nice, does this imply that you must necessarily finish last? Most people give a knee-jerk response to this statement without really contemplating its true import or implications. This statement, along with bromides like "It’s a dog-eat-dog world," serve only both to disempower and force us to believe in false doctrines established by society.
- Teach Your Kids Arithmetic - The Quick-Add - Part I
[Reference-and-Education] Children need arithmetic, particularly in the early years of their education. When they start to stumble in this most important discipline, their attitudes quickly turn rebarbative towards mathematics in general, and their future success in this area is seriously—if not permanently—impaired. With some clever tools, however, this threat is obviated; children are then liberated to succeed in mathematics and prosper in their academics.
- Dabbling in Infinity - Part III
[Reference-and-Education] For those who have followed my series on infinity, this article gets to the crux of the matter concerning the existence of different types of infinity. Having read the two previous articles, you get the sense that the topic of infinity is a strange one indeed. Read through this to the end, ponder its implications, and draw your own conclusions on whether the existence of God is now fathomable.
- Decaying Morals
[News-and-Society] The third millennium has brought with it a new paradigm in society morals, one which, quite frankly, I can live without. Is it just me that sees the steady decay in society morals, particularly with our youth? My principal concern is where we are heading as a nation, as a country, as a people.
- Dabbling in Infinity - Part II
[Reference-and-Education] Boy this math stuff drives me crazy, and I'm a mathematician! John von Neumann, the famous mathematician, said “Young man, in mathematics, you don’t understand things, you just get used to them.” Inherent in this statement is the wonderful truth that mathematics---although difficult---reveals to us many marvelous insights into the world around us. Read this article (Part II of a series) and see whether your perspective on life is not changed one iota.
- The Essence
[Self-Improvement:Spirituality] With all the self-help literature and programs out there, how do we guard ourselves against the endless barage of self-help promises, all asking for a piece of our wallet? What is the essence, the true essence of self-actualization? and what is the one source that we can go to time and time again? Read this and find out.
- Dabbling in Infinity
[Arts-and-Entertainment:Philosophy] Philosophers through the ages have pondered on and dabbled in the concept of infinity. In fact, the Calculus hinges its very essence on this most noble concept. Yet if sets of numbers can shatter our preconceived notions of this idea, which is more or less universally accepted as something real, what more can we uncover by plunging into the mysteries of numbers and mathematics in general?
- Teach Your Kids Arithmetic - "The Nifty Five Square Technique"
[Home-and-Family:Parenting] As a continuation in my series of articles on the merits of mathematics, I submit this topic for consideration by parents who want to give their children a serious edge in mathematics. You see folks, it all begins with the basics. Give your children the basics and then the rest is assured. You cannot build a house on a weak foundation, nor can you expect to build your children’s education on a weak substructure.
- Fun in the Sun - Using Mathematics to Tell Time on the Beach
[Reference-and-Education] Christmas is a week away, temperatures have been hovering in the teens, and I’m writing about fun in the sun and something about using mathematics to tell time on the beach! Good gracious. You must be thinking how weird I am. Well maybe, but for those who have been following some of my other articles, you know then that I seek to show how mathematics—yes even basic mathematics—functions so universally throughout our everyday lives.
- Does God Exist? - A Preliminary
[Self-Improvement:Spirituality] Does God Exist? And if so, what proof do we have? How can we get our faith seedlings to germinate so as to lead to self-actualization?
- Why You Shouldn't Hate Math
[Reference-and-Education] People hate math, at least that's what they're always telling me. Of course, being the way that I am, I have to make converts of everyone. I don't know what my passion is exactly, that drives me to convert the "math haters," but I simply cannot overcome the compulsion to do so. To me, there is not just beauty in mathematics but something else which is spiritual. It's as though God speaks to us through this strange and mysterious language.
- Finding a Mall Parking Spot Using Mathematics - Part II
[Reference-and-Education] Part II of this article gives the curious method to find a mall parking spot using mathematics. Try this out next time at the mall and see how amused you will be. Some of the underlying mathematical theory is cursorily discussed to show how powerful and amusing this subject really is.
- Mathematics and Faith
[Self-Improvement:Spirituality] Just how does an abstract discipline like mathematics find itself mixed up with a notion as difficult to pin down as that of faith. Moreover, how can we show that God's existence is simply an extension of our belief in everyday things that we know exist because of leaps of faith.
- Finding a Mall Parking Spot Using Mathematics - Part I
[Reference-and-Education] If a rudimentary understanding of mathematics can do such a mundane yet practical thing as predicting the wait-time for a parking spot in a busy mall, imagine what else this discipline can accomplish. By opening our eyes to the awesome power of this challenging discipline, we can become effective problem solvers and lead even more effective lives.
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