The Science of Life Lecture Series

In all of science, there are prefixes which are used to are attached to units in order to have a word representation of having differing multiples of 10.  An example of this is the fact that a kilometer is one meter times 1000, or one meter times "three multiples of 10" ($10^3$).  We can also go the other way; a millimeter is one meter divided by 1000, or one meter divided by "three multiples of 10" ($10^3$).  When we have a situation of "divided by $10^3$", as mentioned in the Algebra Lecture Series, it is equivalent to saying "multiplied by $10^-3$".  Notice that the "divided by" has a positive exponent while the "divided by" has a negative exponent.  That stems from the exponent subtraction rule in Algebra. Here's the list of all of the prefixes and what they represent in two numeric forms: Prefix Symbol Multiplier Exponential yotta Y 1,000,000,000,000,000,000,000,0...

In science, there are many numbers which are either exceedingly large (for example, the number of water molecules in a liter of water) or exceedingly small (for example, the charge, in Coulombs, of a single electron).  This is the nature of the reality we live in.  This is why, in some cases, it is easier to read and right these extremely small and large values in a more compact notation.  Yes, this does somewhat reduce accuracy, but the loss of accuracy has very little baring on the accuracy of the final answer.  The most common compact notation in Social Sciences, Life Sciences, and Physical Sciences is called Scientific Notation . The notation for Scientific Notation is $N \times 10^{n}$, where N is a number which is at least 1 but less than 10 $[1 \le N < 10]$ and n is the magnitude of the number.  There are a couple steps to convert to scientific notation: Place a decimal point in between the first two significant digits of the number. Find the m...

Here, I will cover some of the basic operations and properties of real numbers. I say real numbers to differentiate from imaginary and complex numbers, both of which deal with the square root of -1, $\sqrt{-1}=i$. This course will not deal with the square root of -1, so all numbers will be real in this course. There are courses which deal with i, which typically have the word "Complex" in their name. The Absolute Value The absolute value (given by $\left | a \right |$) is the distance from the zero on the number line, regardless of the sign. This is to say $\left | -a |=\left | a |$.  The absolute value of -2 is 2, the absolute value of 2 is 2.  It does not matter what the initial value is, the sign after running it through the absolute value function will always, under every circumstance ever, be positive. Inequalities There are two types of inequality, less than and "greater than".  There are also two flavors of inequality, with and without the equal s...

Algebra is the mathematics of equalities and inequalities.  How much you'll spend at the grocery store, what you'll get on a paycheck after taxes, how much you'll owe or get back in taxes at the end of the year, how much money you'll have left at the end of the month after paying your bills; all of these problems and so many more are, by their very nature, algebraic problems. In this chapter, I'll cover some basics of Algebra and how to problem-solve with Algebra.  Problem solving can be applied to science, economics, and life.  After learning the algebraic problem solving techniques, you should try applying them to the specifics of your life. For those of you keeping track, here's the section breakdown: Section 1: Some Basics of Algebra Section 2: Operations and Properties of Real Numbers Section 3: Solving Equations Section 4: Introduction to Problem Solving Section 5: Formulas, Models, and Geometry Section 6: Properties of Exponents Sectio...