The Science of Life Lecture Series

When interpreting word problems as math equations, it is a good idea to keep in mind that certain phrases will always represent a certain mathematical operation.  Here is a list of some of these words for the basic operations. Addition Subtraction Multiplication Division Equals Exponent Parenthases Add Subtract Multiply Divide Is To the power of Quantity Sum Difference Product Quotient Yields Raised to the Increased by Decreased by Times As much Set as Plus Minus Double ($\times 2$) Halve ($\frac{x}{2}$) Equal to More Less Triple ($\times 3$) A third ($\frac{x}{3}$) Determined to be Combined Change Twice...

If you're familiar with a number line, then you know that each point on that number line corresponds to a number.  If we take two number lines which are perpindicular to one another (they cross each other to make a right angle) and have them cross at the others zero-point, then we have a method of analyzing two-dimensional data-sets and equations, data and equations with two variables which relate to one another.  This two-number-line situation is typically called either the x-y coordinate system (because the horizontal number line is labeled as the x-number line and the horizontal is labeled as the y-number-line) or the Cartessian Coordinate System (named after French mathematician René Descartes, supposedly the first person to come up with the system).  The two number lines, since they're in the context of a coordinate system, are each now called an axis (plural: axes). The x-axis and y-axis of a Cartesian coordinate system. Any point on this coordinate system i...

Graphs are an important part of Algebra since they allow us to visualize information from the equations of Algebra.  After all, we deal better with the visual than the equation.  When we have an equation of two variables, we can see how they relate to one another more readily in a graph than in an equation. The course of Algebra focuses on the concept of functions (which will be defined in Section 2; because yes, functions are different than equations).  Most of the graphs considered here are what is called linear equations, equations which produce lines.  This chapter has the purpose of not only teaching the basics of graphing functions, but also using them for problem solving. Section 1: Graphs Section 2: Functions Section 3: Linear Functions: Graphs and Models Section 4: Other Equations of Line Section 5: Other Equations of Lines Section 6: The Algebra of Functions That's the end of this section.  If you have any questions, please leave ...

Hello internet, and welcome to the Algebra Lecture Series from The Science of Life.  This entry is focusing on conversion of units that you'll see in Physics, Chemistry, Biology, and all of science. Unit Conversion The previous Physics section allows us a mechanism to convert from one unit to another unit of the same type.  To do this, we take advantage of the equivalence between two values, and multiply with what is effectively equivalent to one.  For example, notice that 1hr=60min.  If we divide both sides by 1hr, we get $\frac{1hr}{1hr}=\frac{60min}{1hr}$.  In all of science, units such as seconds, meters, and kilograms can be canceled if in a quotient or squared if multiplied together, much like variables.  With that in mind, notice that on the left hand side, the hours cancel and the ones cancel, so that we have $1=\frac{60min}{hr.}, which makes sense since there are 60 minutes per hour.  This general concept applies to all conversion facto...

Hello internet and welcome to the General Chemistry Lecture Series from the Science of Life. Today, I will cover the study of chemistry, which is the study of the properties, behaviors, and interactions of matter, which is the physical material of the universe. A property, from a chemistry point of view, is any characteristic which helps us to distinguish a substance from other substances.  Examples include the fact that water is liquid distinguished it from ice (a solid), the fact that water is clear distinguishes it from random non-Lemon-Lime soda (a non-clear liquid), the fact that water has a density of 1 kilogram per liter which distinguishes it from sulfuric acid (which has a density of 1.84 kg per liter), the fact that water has a chemical composition of H 2 O which distinguished it from Hydrogen Peroxide (which has a composition of H 2 O 2 ), and the fact that water is tasteless which distinguishes it from hospital coffee.  These are all examples of properties, but i...

Hello internet, and welcome to the introduction to Chapter 1 of General Chemistry.  This chapter is going to set you up for success in chemistry in general, as it will be well used in all chemistry courses.  Most of this chapter will also be used in all of science, but there will be parts which are chem-centric. Chemistry is the study of the materials of the universe and the changes which those materials undergo.  One of the joys of chemistry is seeing how the principles of chemistry applies to all aspects of everyday life, from cooking and burning of gasoline (petrol for my European readers) on the individual level to the development of medications and the growing of crops on the far-reaching end. This first chapter lays down the foundation required for success in any science in general and chemistry in particular.  This includes fundamentals of chemistry, matter, and scientific measurements.  Keep in mind that the information in this lecture series ...

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 describe some of the basics of algebraic manipulation.  First, we need to define a formula, which is any equation which uses letters to represent relationships between quantities.  An example of this is the area of a circle, $A=\pi r^{2}$.  You'll remember from Section 3 that we can solve for a variable.  The formula I used was the one relating masses of two object, their distance, a constant, and the Gravitational force. To solve a formula for a particular variable or constant, perform the following steps: Multiply both sides by any denominator there happens to be in order to cancel out any denominator and clear any fractions.  Combine like terms. Using the addition principle, get every term with the variable to be solved for on one side of the equals sign and every other term on the other side of the equals sign.  Combine like terms again if necessary, which may include factoring. Solve for the variable by using the multiplicatio...

Hello internet, and welcome to the Algebra Lecture Series from the Science of Life.  This entry is an introduction to algebraic problem solving.  In Algebra, there are five steps for problem solving, which I'll cover here. Familiarize yourself with the problem situation.  This is basically a situation of knowing what the context of the problem is.  Is the context taxes?  Grocery shopping?  Tipping?  Scaling up or down the ingredients of a cake to get a different size cake than what the recipe says the size will be?  Here are the sub-steps for this contexts step: Read the problem carefully.  Read it aloud if need be to understand the problem. List the information and state the question being asked.  Select variables to represent anything which is unknown and clearly state what the variables represent, and be descriptive about the statement. Obtain any relevant information and equations.  If you're painting a room, find the ...

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...