What is Reddit's opinion of How Not to Be Wrong: The Power of Mathematical Thinking?

Unfortunately, you're probably going to find yourself in deep trouble.

Math is a progressive subject, meaning that mastery of earlier material is normally necessary to understand later material. Indeed, you'll discover that almost everyone - no matter how smart - eventually hits a wall where they just don't understand enough of the foundational material for certain new material to grasp it at more than a fuzzy level.

Moreover, math is much, much easier to learn when you're young. It's like language in that way.

Now, from the standpoint of becoming an educated adult, I'd highly recommend books like How Not to Be Wrong that will give you an overview of mathematical concepts without requiring you to understand the underlying material all that well - you can just take a lot on faith.

But that won't help you pass your general education requirement.

Now, there are two ways to go about this. The first is to spend a lot of effort mastering the material you didn't master the first time.

The second is to just try to get past that one course you need to take in your non-quantitative major. For students in your situation, this is normally the best course of action.

It's also advisable to not take this one course at the college you'll be attending. Instead, check whether you can transfer in credit and try to take the course at a Community College. Normally such schools offer as much grade replacement as you want - you could take the course 20 times until you finally passed - and the grade won't affect your GPA when it's transferred in.

You should read Jordan Ellenburg's book How Not to Be Wrong: The Power of Mathematical Thinking. I have a feeling you'll enjoy it a lot, and you're the target audience. Put it on your Christmas list! This is kind of a TLDR, but my longer answer is below.

I'm not a mathematician, so you may find my color on this subject intriguing. I majored in math as a second major purely because I wanted the background I'd gain from a math major for other pursuits. My primary interest as a sophomore/junior in college was geodesy, a subject which Gauss and Laplace both made profound contributions to while they simultaneously reshaped the way we think of probability (Laplace made Bayes' theorem practical), statistics (the bell curve is a Gaussian distribution, which is ubiquitous), differential equations (especially Laplace), number theory, and calculus. I picked up math as a second major while primarily focusing in geomatics, which heavily incorporated geodesy. But I didn't stick with that subject, and today I work in a field completely unrelated to Earth science.

Today I manage a bioengineering lab. But I can tell you that majoring in math was extremely beneficial in my undergrad studies (it frankly made every numerical exercise in geomatics quite trivial), and it continues to be helpful to me now. Today I use my math background to help my engineering colleagues work out difficult simulations, to do statistics, and to write code for data analyses. That's to say, you can't foresee how a math major is going to benefit you. (I've even been told several times that law schools prefer math majors over most other majors because of the rigor that a math major can approach problems with!) I'm grateful for my math education every day where I contribute to the research in my lab (which is a very minor part of my job).

From my experience, I want to focus on what you'd do if you went to grad school in the mathematical sciences (math, stats, CS). At the undergraduate level, majoring in math is the best prep you can undertake for graduate study (in mathematical sciences). I had classmates who pursued second degrees in engineering; went on to become accountants, actuaries, or programmers; and some who went to grad school in math or CS or astronomy. I personally plan to go to grad school in statistics. In these examples, math is often the best preparation you can undertake for future studies. In the hardcore math sciences, the math you do as an undergraduate is a total prerequisite for graduate study, and when you switch disciplines you'll pick up on the theory faster than any of your classmates do.

Physicists hold a special exception to the rule I'm describing that I think is worth mentioning. A physicist is trained to think in terms of differential equations and experimental errors perhaps better than anyone else who uses math at their level of rigor. I have a lot of envy for physicists in this regard.

The other point I'd make is that the proof you cited is purely pedagogical. It's that precise to show how precise math can be. In practice you'll rarely need to use that precision. The precision of the proof you cited is entirely intended to indoctrinate undergraduates to the nuance that can be needed in thought. But when you're a graduate student or a researcher working on problems that only 100 people worldwide can understand, your proofs are outlines that more closely resemble the proof you described as your intuitive one. That is, if you're doing research level math, you get to assume a lot about the ability of your readers.

You're young. Eventually, though, you'll reach a point where you're writing to an audience with the same education/expertise as you, and you'll be able to gloss over the trivially obvious points. Your undergraduate studies will not be that point. In undergrad, the emphasis is on forcing you to think as atomically and precisely as possible. During that time, you need to demonstrate as many details as possible in a proof to show that your intuition is logically justified. But again, at some point (possibly around PhD candidacy), you reach a point where your proofs become outlines of a much more rigorous proof that someone could formalize if they wished to.

I'd say it's great to major in math. My experience studying math shaped the way I think about problems in a way that is very unique compared with my peers. If you're really concerned by the value of the degree later, double major in something more equitable like engineering. But I promise you'll be grateful for your background in math after graduation.

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What is Reddit's opinion of How Not to Be Wrong: The Power of Mathematical Thinking?
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