Questions tagged [graduate-education]
For questions related to studies for graduate or more-advanced students and courses.
90 questions
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Is MacLane and Birkoff's "Algebra" suitable today as either an undergraduate or graduate text in abstract algebra?
I'm going to review the 3rd edition of Saunders MacLane And Garrett Birkoff's Algebra at my blog soon and this is the first time I'm really carefully reading it. While I'm really enjoying the book,I'...
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Where can I find new types of problems regarding graduate level mathematics?
Though not an undergraduate student , I just wanted to know where can I find hard new types of problems regarding the problems in graduate level mathematics.
As per my information , standard books ...
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When learning about algebra and geometry, should I read roughly or try to understand every sentence?
I am a new graduate student majoring in pure mathematics. In past four years, I was interested in analysis, especially complex analysis. Now I think what attract me most are topics about algebra and ...
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Math programs in Russia and post-Soviet states - how do they compare to US?
I studied math in college and also took a few years of Russian. For a time, I was looking for a way of living in Russia post-graduation (well before the recent war) and I asked one of my professors, ...
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What can I do when advanced undergraduate and/or early graduate STEM students cannot perform correct math manipulations?
I have helped to TA and taught several courses with mixtures of advanced undergraduate and early graduate students in engineering/STEM. These courses are the classics: signal processing, control, ...
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Book recommendations for Math for Biochemistry Course
I am a mathematics teacher currently teaching at highschool level. I have taught at college level and I do have some preparation about topics such as differential equations and multiple integrals. ...
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Resources for designing math degree programs
I'd like to know where I can find resources which are helpful when one has to design or improve grad and undergrad degree programs in pure and applied mathematics.
In particular, I'm searching for up-...
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Are the standard of questions provided in reputed institutions like MIT, Stanford, Oxford, etc., as good as the problems of IMO?
I did not win the International Mathematics Olympiad, so I was very curious to know the standard of questions asked in the graduate and undergraduate courses of maths and computer science in ...
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Strategies for Designing Challenging Yet Feasible Quiz Problems for Upper-Level Math Courses
In the past semester, I taught two 7-week courses: discrete math and algorithms designs (which is essentially still math) for undergraduate CS students. I implemented weekly 25-minute quizzes ...
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Summer or Semester Programs which bridge to Graduate Mathematics
A few years back I had a student attend the MASS semester at Penn State. It was a fantastic experience for my student and it certainly helped him find a place in graduate school and I would wager it ...
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Books with Glossaries
I am seeking example math books that have a glossary.
I would especially be interested in an example that has a list of symbols,
a glossary, and an index.
I am working on a book (aimed at graduate ...
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Mental Health in Mathematics
I am not sure if my question is relative to this meta but I still want to put forth my thoughts and concerns and questions because I think its not just me but others too who have similar issues.
My ...
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If I take Modern Analysis next year, will I be prepared to teach multivariable/vector calculus?
I’m currently getting my Master’s in Math at Portland State University so that I can teach community college mathematics. I’m specifically hoping to teach calculus, statistics, and linear algebra, so ...
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Common mistakes in probability
$\DeclareMathOperator\Var{Var}\DeclareMathOperator\Bern{Bern}\DeclareMathOperator\Pois{Pois}$Question: What not-trivial mistakes do students often make when solving problems in probability theory, ...
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What is gratifying in being a mathematics teacher?
I think the title says it all, but in case it does not:
Is being a math teacher gratifying?
If yes, what is gratifying in being a math teacher? (If not, why...)
Does the feeling lasts, or perhaps ...
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14
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Teaching advanced math using books with cartoons
Could an effective and 'comprehensive' course on advanced math be taught through a series of fun comic books, say a fun and adventurous series of stories each exploring advanced math principles ...
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6
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What are some ways that one can progress from stage 2 to stage 3 of the rigor stages that Terry Tao has described?
Terry Tao describes 3 stages of one's mathematics education on his web blog.
1: Pre-rigorous
2: Rigorous
3. Post-rigorous
I know how one can progress from stage 1 to stage 2 (this simply can be done ...
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Why is multivariable analysis often omitted?
Related but not duplicate: What courses require multivariable analysis?
By multivariable analysis I mean the rigorous version of multivariable calculus (something equivalent to Ch.9-10 in baby Rudin ...
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What are some research-level opportunities in mathematics that do not focus on proofs?
The research level of mathematics (what is done by professors and upper-level graduate students) tends to be heavily portrayed as focused on writing proofs to the exclusion of most anything else math-...
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Which books on geometry and topology are best for teaching an intro graduate course?
I'm teaching a graduate (Master's) introduction to geometry and topology (e.g. some basics on manifolds, vector bundles, algebraic topology). What textbooks have you found are best for teaching a ...
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Is the Wronskian still assumed for graduate education?
About thirty years ago, in a practice GRE (Graduate Record Exam) math
test in the US,
a question assumed the student knew the definition of the Wronskian. I had never heard of this determinant
before.
...
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Conferences dealing w/challenges of teaching higher level math to STEM audiences
I'm interested in knowing whether there are conferences that have, among other topics, the difficulty of teaching higher level mathematical concepts to folks with prior established skills in STEM, e.g....
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1
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Is it weird for an undergrad or grad quant/applied maths(/even pure maths) programme to not teach that probabilities of 0 or 1 will never change? [closed]
Edit: i didn't mean it like this programme should do this or that. i mean other people are accusing me like 'your programme should've had this or that' (actually they're saying that i should know this ...
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What are some good examples to motivate the implicit function theorem?
I always had problems teaching the implicit function theorem in advanced analysis courses. This result is motivated by later applications, but it would be great to provide easily accessible examples ...
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3
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1
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To what degree can the legally blind, with computer induced medical problems, study statistics?
My son graduates from secondary school in 2022. But he shall attend university in Australia or UK — where you must apply for ONE major — not liberal arts in the USA. He wants to pick BSc Math with ...
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3
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2
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Succinct description of situations where naively obvious is correct, but for far more complicated reasons?
What is the name for a situation where the obvious thing turns out to be true, but the reasoning is more complicated?
In abstract algebra we can say the rational numbers - the fractions, $\mathbb{Q}...
CommunityBot
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8
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How do I learn advanced mathematics without forgetting?
I am pursuing mathematics through distance education and I find that it takes me a long time to understand the concepts (e.g. sigma fields, measure theory, connected topological spaces, etc.).
After I ...
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7
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Galois Theory: necessary?
I noticed the discussion of whether the teaching of Galois Theory is necessary on MathOverflow. Here at LSE, everything we teach in mathematics should have some application to the social side of life.
...
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What famous graduate math textbooks use color?
I know that undergrad math books use colors, like Gilbert Strang in his undergrad Linear Algebra textbooks and Measure, Integration & Real Analysis by Sheldon Axler. Many first year calculus ...
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When to encourage students to read mathematical literature written in English (in non-English speaking countries)?
There is a lot of mathematical literature in some non-English languages (French, German, Spanish, etc.) that students from these countries don't need to read English literature (at least) for their ...
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How much more skilled in the topic should you be in order to teach the topic?
For sake of argument, consider that skill of a topic is spectrum from "new and learner" to "experienced and expert." Where should you relatively be in order to teach the topic ...
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Is SQL relevant to statisticians' work?
I hope this is the right place for posting this, but if not, please let me know!
I recently took a second class in Python programming which, toward the end, also taught a little bit of SQL. As it ...
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A Question about Theodore Frankel's "The Geometry of Physics"
Locked up in my self-distancing isolation in NYC, I'm reminded of how much I really like Frankel's book, which contains a wealth of beautiful geometry and topology from the standpoint of a ...
CommunityBot
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3
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Evaluating textbooks in math and physics
I’m currently interested in textbooks, especially the ones in math and physics that are used at the high school, undergraduate and graduate levels and, given the experience of the people on this ...
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Data on textbook adoptions in universities (math/science)
Does anybody know if there is a website/database/... on textbooks adoption in the US or some other country? (math/science textbooks)
It would be interesting to see which textbooks are (and have been) ...
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What does one full year of calculus mean?
If a masters program (Fordham in math education) requires "at least one full year of calculus" does that mean just calc one or more than that?
2
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0
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Why are a.e. defined functions rarely mentioned in elementary books?
In any standard development of measure theory in several well-known textbooks, the use of almost everywhere (a.e.) defined functions are first seen in the statement of Fubini's theorem, which states, ...
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MacLane-Birkhoff's "Algebra" vs Jacobson's "Basic Algebra I,II" vs Lang's "Algebra"
(Cross-posted at Math.Stackexchange)
I'm searching for an apt textbook(s) on Abstract Algebra for a very advanced undergraduate/graduate level course in Algebra, and would be grateful for any help. ...
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Online open-course-ware that uses Maclane's book "Algebra"
I am struggling with that book which I find to be more of second-guessing type than a book for self-study: it has cryptically written sections, no examples (and those given, and rarely, are even more ...
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4
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3
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Geometry textbook with an abstract algebra emphasis
I'm teaching a variety of undergraduate and graduate geometry classes (mostly for in-service teachers) which range from elementary axiomatic geometry to more advanced transformational geometry. I'm ...
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Are students majoring in pure mathematics expected to know classical results in mathematics very well by their graduation?
For example, I am confident that very few students majoring in pure mathematics can write a complete proof to the Abel–Ruffini theorem (there is no algebraic solution to general polynomial equations ...
3
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On concentration inequalities [closed]
I would like suggestions for a good text on concentration inequalities (examples here https://en.wikipedia.org/wiki/Concentration_inequality). I am looking for sources (texts) that can give strong ...
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Better strategy on math graduate school [closed]
I'm just starting graduate school (master in mathematics) and there we have absolute freedom in choosing the number of courses that we can attend each term. In consequence, I'm wondering what is the ...
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Quizzes (with questions known in advance) instead of homework in a graduate mathematics class. Good Idea or Bad Idea? Pros and Cons?
I'm teaching a graduate course in mathematics next semester. I'm planning to have a midterm and a final exam. But I'm thinking about having weekly (or once-every-two-weeks) in-class quizzes instead of ...
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Why do the stages of rigorousness have specific timestamps?
This is a reduced quote from There’s more to mathematics than rigour and proofs of Terrence Tao (emphasis mine):
The “pre-rigorous” stage, in which mathematics is taught in an informal, ...
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Using Several Textbooks in a Course
Sometimes a teacher prefers to use several textbooks in his/her courses because he/she thinks the arguments of each book is better in a part of course material or there is no comprehensive textbook in ...
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1
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Effective computer lab layouts for a university math class
Many math classes benefit from occasionally being held in a computer lab. My question is about the pros and cons of different layouts and mechanics of a lab and "solutions" you have found to be ...
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How much prior math should I review in teaching a graduate-level course?
I am scheduled to teach a graduate-level course in engineering whose basis is in the solution of ODE’s and PDE’s, and thus is about halfway between a math course and an engineering course.
We ...
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L'Hopital's Rule: Why do we need it?
I'm preparing a design/teaching experiment for my Curriculum Design Course right now. I've decided to cover L'Hopital's rule with a student I've been working with for a year, so skill wise he's ready ...
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A4 paper of notes in an exam
What are the effects of allowing students take one paper, say of A4 size, full of whatever they want, into an exam? It might be called a cheat sheet or something similar. Students might write it by ...
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