<p>Hey, I've always been good w/ math and am thinking about minoring in it. The problem is that I have no clue what each class is about and don't want to walk into a class without knowing what it is first. I am tried wikipedia for some, but for others I couldn't find out what they are. Here is the list of classes I could take:</p>
<p>Calc 3
Intro to Differential Equations
Linear Algebra
Intuitive Topology
Discrete Mathematics (is it like finite?)
Elementary Computational Methods or Methodology
Modal Logic
Intro to Mathematical Reasoning</p>
<p>To earn a minor I need to take 2 of those classes. Which classes would you recommend? Which are the easiest/hardest?</p>
<p>Well, I can only give you a one-sentence summary either, but I hope it will make more sense:</p>
<ul>
<li><p>Calc 3: Calc 1 and 2 were about functions from the reals to the reals (something 1-dimensional). Calc 3 generalized these concepts to more dimensions. For example, in Calc 1 or 2 you learned how to compute the arc length of a curve. In Calc 3 you would learn how to compute the area of a surface. (Think crumbled up piece of paper.) </p></li>
<li><p>Differential equations: they are something very useful in applications. Take for example a cooling problem. Suppose the function T(x) stands for the temperature of an object at time x, and suppose you know that the “cooling rate”, how much the temperature decreases with time (= - dT/dx), is proportional to the temperature, i.e. - dT/dx = kT(x). (This makes sense intuitively: 200 degree hot water will lose 10 degrees faster than 100 degree warm water.) Now you would like to find an explicit formula for the function T that satisfies these conditions. Differential Equations will give you tools to do this.</p></li>
<li><p>Linear Algebra: It’s very important for most higher math as well as applications. In essence it’s very simple: you study linear functions (y = ax) in higher dimensions and the spaces in which they sit, called vector spaces. Euclidean 3-space with an x,y,z coordinate system is a vector space. Linear algebra classes often have a computational focus (it’s all about matrices, if you happen to know what those are), or you might prove some of the fundamental results about vector spaces and linear transformations that multivariable calculus is built upon.</p></li>
<li><p>Topology: Topology is sometimes called “rubber-band geometry”. In geometry you pay very much attention to local properties of an object, e.g. angles and the length of sides. But if you tried to examine every single item in your room this way, you would be exhausted pretty fast. Topology takes a less ambitious approach and tries to classify objects by their “general shape” only. For example, a circle and an ellipse have the same general shape, and we include all other squiggly lines that do not intersect themselves. It’s easy enough to deform a piece of string in the shape of a circle into an ellipse or other squiggly circly things. A donut and a coffee mug also have the same general shape because they are both 3-dimensional objects with exactly one hole. Topology develops a set of tools that help you decide whether two objects have the same general shape. (By the way, “same general shape” means that there is a nice invertible continuous function between the two objects, called a homeomorphism.)</p></li>
<li><p>Discrete Math: You are right, discrete math is finite math. Discrete Math usually covers a whole array of topics. One of them is combinatorics and probability: how many ways are there to park 6 cars in 10 parking spots? What are your odds of winning the lottery? You might also learn some number theory. (Did you know that there exists at least one prime number in between 200 and 400, or 10 million and 20 million or n and 2*n for any natural number n?) Discrete Math is often used as an introductory proof-writing course, so you would probably also do some basic set theory, mathematical logic, induction, etc.</p></li>
<li><p>Intro to Mathematical Reasoning. This sounds like an intro-to-proof course, which is very helpful to take before real analysis and abstract algebra. At my college I would tell you to skip it and take Discrete Math or Number Theory instead because those courses teach the same concepts in a much more interesting way, but your college might be different.</p></li>
</ul>