Math (short for mathematics) is a study of operations involving numbers, which can be applied to various situations in which one would desire a quantity, rate, distance, time, weight, or so on.
Men have been using math for millennia to solve problems, such as finding how many steps should be in a staircase, measuring the proper dosage of anesthetic, determining the market value of a commodity, finding distance between celestial objects, and programming the device you are using to read this sentence.
Math studies Edit
There are several different studies of math, with differing applications.
- Arithmetic - The simplest branch of math, arithmetic involves elementary operations such as addition, subtraction, multiplication, and division. In the traditional western educational system, one typically learns arithmetic starting in elementary school.
- Algebra - Algebra involves the manipulation of equations to find the value of a variable. Students typically start learning algebra in middle school.
- Geometry - Geometry is a mathematical study involving shapes, and can be somewhat formula-heavy. Students typically learn this topic in middle or high school.
- Trigonometry - Trigonometry is the mathematical study of triangles, and can be quite heavy on the formulas. Trigonometry is typically taken in high-school. Trigonometry is sometimes a prerequisite for Calculus.
- Calculus - Calculus is a course that many people find intimidating, as it involves many concepts that may be completely new to the student. Calculus is the mathematical study of the function of variables. It can be taken in high school, though many students have their first calculus course in college. College students don't usually take calculus, however, some majors require it. For example, some engineering majors require three calculus courses.
Virtually all of the above may be taken as college course, even arithmetic as a discrete math course. However, such college courses may be more in-depth than their K-12 counterparts, and may focus far more heavily on practical application and number theory.
"When will I use this in life?"Edit
Until you get to college, you'll likely hear someone ask "When will I use this in life?" at some point during a school year in which you have a math course. You probably won't hear this at all in college, because the ones who don't see the value in math will mostly be filtered out through the process of admissions, while the rest of us will have figured out a few things about it.
While a lot of us would prefer to avoid all the big, scary-looking math, the jobs wherein one uses math tend to pay well, because there are fewer people out there that have demonstrated during their education a proficiency in using more complex math. Of course, a person can "get by" with a low-paying job that is a result of a lazy education, but "getting by" doesn't always mean "having a nice car", "having a bigger home", "getting married", and "having sex". If these things sound nice to you, they'll be easier for you to have if you can obtain a better-paying job. And getting a better-paying job is much easier for those who can do math.
Useful things to know Edit
The following is a few useful tips if you're interested in getting better at math, perhaps because you're interested in a career change. These are very basic tips, however, but they might help someone.
- Know the order of operations when solving a problem. You might notice that if you see a problem with both addition and multiplication, the answer would likely be different. This would make no sense. It matters what order you perform operations. In most cases, what's in parentheses is operated on first (that's what parentheses indicate in math). Next, calculate any roots or exponents (roots and exponents are inverse operations, so the order between the two doesn't matter). Next, perform any multiplcation and division, then perform any addition and subtraction. Perhaps the most useful mnemonic for remembering the order of operations is "PEMDAS" (short for Parenthesis, Exponents, Multiplication, Division, Addition, then Subtraction).
- If you do something to one side of an equation, make the appropriate change on the other side. Sometimes, this is what it takes to solve a problem. If you subtract 4 from one side of the equation, subtract 4 from the other side, as well. When dividing one side by 5, divide the other side by 5. After all, the equal sign indicates that both sides of the equation are equal in value. This may be what it takes to put a variable by itself on one side, so the other side can be simplified to find its value.
- Start small and practice. A lot of aspiring mathematicians try to take on calculus concepts early because they think they can handle it, then they become frustrated when they don't immediately figure something out. The easier concepts toward the beginning are intended to prepare students for what's ahead. Familiarize yourself with the basic before taking on the more challenging stuff, and drill the basics later on, if need be.
- The idea behind math isn't to become a nerd, it's to become good at doing something. If you're looking for a career change, it's not a bad idea to pick a skilled trade to look into in addition to your math studies. Once you've picked a trade, look into how that trade uses math.
This section contains a few definitions of math phrases so you can participate in a discussion involving math, and sound like you'll have some idea what you're talking about. It can also spare you from having to give up your man card when it's discovered that your elementary school child is better at math than you.
- Coefficient - A coefficient is a number next to a variable in a term showing that the variable is to multiplied by that number. For example, in 3x, three is the co-efficient.
- Difference - A difference is a result of subtraction. For example, the difference between seven and four is three ( 7 - 4 = 3 ).
- Equation - An equation is an expression with an equals sign ( = ). Remember, an equals sign indicates that the expression on the left of the equals sign is the same value as the expression on its right.
- Exponent - If you see a small, elevated number next to a number or variable, the small number is an exponent. The exponent shows how many times that number is to be multiplied by the same number. In typing, an exponent is a number to the right of a caret (^). So in 3^4, 4 is the exponent. The term 3^4 is another way of writing 3 * 3 * 3 * 3, the product of which is 81.
- Expression - An expression is a mathematical problem, including all the signs, numbers, and the equals signs, if an equals sign is present. An example of an expression is: 3x + 2x^4 + 12.
- Fraction - A fraction is another way of expressing division. At a certain point in one's education, long division becomes infrequent, fractions become commonplace, and the "divided by" sign almost entirely falls into unuse. An example of a fraction is 1/2, which in decimal form would be represented as 0.5.
- Integer - An integer is a non-fractional, non-decimal number, either positive, negative, or zero. It's what is referred to as a whole number. Examples of integers include: -2, -1, 0, 1, 2.
- Irrational number - An irrational number is a number that can't be represented with a simple fraction, and when written with a decimal, the sequence of numbers would continue on without terminating. A couple well-known examples include Pi and the square root of 2.
- Natural number - A natural number is a non-negative, non-fractional counting number greater than zero. When a variable is known to be a natural number, the letter "N" is used. Examples include: 1, 2, 3, 4, 5.
- Product - A product is the result of multiplication. The product of four and three is twelve ( 4 * 3 = 12 ).
- Quotient - A quotient is the result of division. When eight is split four times, the quotient is two ( 8/4 = 2 ).
- Rate - A rate is a measurement (such as miles or kilometers) divided by another variable, usually time. For example, sixty miles per hour is a rate, and it (60/1) means that someone travelling at that rate (speed) is travelling sixty miles in an hour, or one mile in one sixtieth of an hour.
- Sum - A sum is a result of addition. The sum of eight and six is fourteen ( 8 + 6 = 14 ).
- Term - A term is a number separated by signs indicating addition and subtraction. For example, in 4x + 6 - y, the terms are 4x, 6, and y.
- Variable - A variable is a number with a value that may initially be unknown, or with a value that may depend on another variable, therefore, a letter such as "X" is used as a placeholder. Much of algebra involves finding the value of variables by manipulating other terms in an expression.
- Vector - A vector is a rate and a direction. If something is travelling with the same speed as something else, and is travelling in the same direction, then both objects have the same vector. Similar vectors that are drawn in a line would be parallel.
Facts about mathEdit
Many people wouldn't think that math could be interesting, but those people would be mistaken.
- The Pythagorean theorem - There existed a cult in ancient Greece called the Pythagoreans, who carefully guarded a mathematical secret: A^2 + B^2 = C^2. That would be the formula we use today to determine the length of a side of a triangle with a right angle. One man leaked the secret, and he was subsequently murdered. Meaning that someone actually died over this.
- The Fibonacci sequence - Seemingly simple, this sequence is written out by adding the previous two numbers in the sequence, with the first two numbers in the sequence being 0 and 1. It would look like: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34... The Fibonacci sequence appears in nature, such as in patterns in the leaves on a stem, and the fruitlets of a pineapple.
- Pascal's triangle - Pascal's triangle is a trianglular arrangement of numbers in which the next number down has the value of the two numbers directly above it (one on the left, and one on the right). Many patterns have been found in Pascal's triangle, including that the Fibonacci sequence can be found by summing the shallow diagonals in descending order.
- Menger sponge - A Menger sponge can be seen as like a Rubik's cube with the middle pieces and core removed. This would be called a "level 1 Menger sponge". A level 2 Menger sponge would be like cutting a similar pattern into the remaining pieces. Repeating the pattern once more would result in a level 3 Menger sponge. A cube could be seen as a level 0. If submerged in water, drying a level 4 Menger sponge would be very difficult.