21

Memorization per se should not be the primary focus. When I learn something new, I type up notes on the computer in a reverse-indented outline format. Then as time goes on and my understanding improves, I edit the notes to reflect that. When I work an exercise or read a paper, I refer back to my notes. Memorization, to the extent that it happens, is just a ...


16

For context, I have a lot of experience self-learning mathematics. I spent a summer learning additional algebra, point-set topology, linear algebra, and analysis (to extend my undergraduate degree) before entering my current graduate program. This was sufficient to skip a literal year in the program. I am now well into the program and have to self-teach ...


10

Asking random math educators about the policies of a specific graduate school makes absolutely no sense at all. The page you were looking at has this contact information at the bottom. Use it! Adolescence Mathematics Contacts 45 Columbus Avenue 2nd Floor New York, NY 10023 Tel: 212-636-6400 Fax: 212-636-7106 Email: gse_admiss@fordham.edu Dr. Alesia ...


8

In the US, the stereotypical "one year of calculus", means "calculus one" and "calculus two" (semester system). It would rather approximate what is in AP Calculus BC, except perhaps without graphing calculator use. It would include basic differentiation and applications of differentiation (max/min, rel. rates), integrals, special techniques of integration ...


7

1) Primarily I choose textbooks based on the needs of the class (and the students's backgrounds and goals) and what it is preparing for. For high school, if it's for AP tests or IB tests at the end of the year, I'll very likely try to find textbooks (or materials) that explicitly state they help prepare students for that. The best books contain questions ...


5

The Open Syllabus Project presents a large amount of data about books listed on syllabuses of courses taught around the world (especially in the USA and not only about math/science). I think that it is not possible to ensure that the presented textbooks are indeed the most adopted (or bought or sold or used or read). However, they probably are (at least) ...


5

For about 25 years, in upper-division undergrad as well as graduate courses, I have created notes to accompany all courses I give. Yes, this takes some energy. Also, by the time I started this, I'd been teaching such courses for almost 20 years, so had some experience. Especially after it became possible to create typeset notes as fast as one could type, ...


5

Do statisticians use SQL in their work? Yes! I would say it is already prevalent. Four indications: One is how SQL queries are now easily accessed from within R: Database Queries with R. You are apparently already familiar with Python and SQL interfaces, e.g., SQLite. There is a DataCamp course Introduction to SQL. If you are on the job market as a ...


4

I teach at community college. That means I have a masters degree. When I first taught statistics, I had never taken a statistics course. Luckily, it was before I adopted my son. I spent 60 hour weeks, studying from many different textbooks, and asking myself questions. (I proved some results that we would never prove in our stats class.) I was an ok teacher ...


4

I've owned the revised first edition of Frankel's The Geometry of Physics: an Introduction at least since I was a graduate student. The texts I suggest in this answer are largely based on my personal library. Part I: Manifolds, Tensors, and Exterior Forms Contains 6 chapters which construct the canvas on which the later part of the text plays out. I'll ...


4

I teach at a community college, so all of what I have to say applies to the first two years of undergraduate study. I've been trying for years to get my department to consider OER (Open Educational Resources) aka books that are Creative Commons instead of copyright. Our students are usually on very tight budgets, and cheaper books means less hours at a low-...


4

For most people, including myself, there is pretty much no chance that you’ll remember most of the things you’ll see and do in math-land the first time ‘round. It’s just an inevitable relic of the fact that mathematics is... well... hard, and it isn’t something that the human brain was designed to do. The fact that you’ve gotten as far as you have is an ...


3

You don't describe engaging in conceptual chunking. You mention the Sylow theorems as an example and I will also use them as an example. It is easy enough to memorize the theorem statements. If you do not chunk the material in the proofs, then I challenge any claim that you understand the proofs. (Fix a positive prime integer, $p$.) The Sylow theorems ...


3

There is no generally applicable answer to your question. In my own career I often taught while learning the material as my mathematics department began to offer more and more computer science. I learned the material a course at a time by signing up to teach it. I talked a lot with colleague mentors who knew the material. I always told my students in the ...


2

I think it is important to do some drill EVEN (maybe especially) with advanced concepts. This is because the concepts may be more strange and abstract. So you need to do some basic work to get familiarity with it. Quantum mechanics (or E&M) are rather non-intuitive and you just need to work with them. Not everything is as much an "aha" ...


1

I believe you should follow these steps: Understand what the theorem says, with some applications of it (which also means to do the exercises, also show your work to TAs) Try to prove it yourself and get stuck quickly Work through the proof and try to understand it Take a fresh sheet of paper and now try again to do the proof When you get stuck (which you ...


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