Questions tagged [graduate-education]

For questions related to studies for graduate or more-advanced students and courses.

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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. ...
NotAMathematician's user avatar
6 votes
1 answer
457 views

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-...
Uagi's user avatar
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-4 votes
1 answer
244 views

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 ...
Sillyasker's user avatar
5 votes
1 answer
223 views

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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3 votes
2 answers
2k views

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 ...
Sillyasker's user avatar
1 vote
1 answer
100 views

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 ...
James S. Cook's user avatar
24 votes
14 answers
17k views

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, ...
Fraïssé's user avatar
  • 737
3 votes
0 answers
116 views

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 ...
Joseph O'Rourke's user avatar
7 votes
4 answers
2k views

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 ...
blakedylanmusic's user avatar
3 votes
2 answers
353 views

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, ...
Botnakov N.'s user avatar
6 votes
1 answer
311 views

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 ...
Mike's user avatar
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5 votes
1 answer
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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 ...
David Corwin's user avatar
15 votes
11 answers
4k views

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-...
Robert Columbia's user avatar
4 votes
2 answers
1k views

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. ...
Joseph O'Rourke's user avatar
5 votes
1 answer
101 views

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....
Russ's user avatar
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1 answer
165 views

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 ...
BCLC's user avatar
  • 574
4 votes
1 answer
457 views

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 ...
False Equivalence's user avatar
3 votes
1 answer
195 views

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 ...
Wes's user avatar
  • 133
8 votes
1 answer
894 views

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 ...
user avatar
21 votes
8 answers
7k views

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 ...
user avatar
8 votes
2 answers
459 views

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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3 votes
1 answer
170 views

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 ...
Ricky_Nelson's user avatar
9 votes
2 answers
2k views

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 ...
The Mathemagician's user avatar
6 votes
1 answer
126 views

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) ...
lorenzo's user avatar
  • 251
9 votes
3 answers
325 views

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 ...
lorenzo's user avatar
  • 251
2 votes
2 answers
1k views

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?
Burt's user avatar
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2 votes
0 answers
156 views

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, ...
RandomStudent's user avatar
8 votes
3 answers
2k views

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. ...
user avatar
2 votes
0 answers
280 views

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 ...
André Gargoura's user avatar
4 votes
3 answers
402 views

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 ...
Jeremy Brazas's user avatar
9 votes
3 answers
3k views

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 ...
Zuriel's user avatar
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3 votes
2 answers
307 views

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}...
john mangual's user avatar
3 votes
0 answers
127 views

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 ...
batwing's user avatar
  • 139
3 votes
1 answer
266 views

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 ...
HeMan's user avatar
  • 251
13 votes
3 answers
293 views

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 ...
MichaelGaudreau's user avatar
3 votes
1 answer
609 views

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, ...
Ooker's user avatar
  • 183
2 votes
1 answer
198 views

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 ...
Maesumi's user avatar
  • 1,390
9 votes
2 answers
202 views

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 ...
aeismail's user avatar
  • 199
5 votes
3 answers
424 views

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 ...
Mary T.'s user avatar
  • 59
9 votes
3 answers
2k views

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 ...
Tommi's user avatar
  • 7,015
16 votes
1 answer
284 views

How to improve atmosphere in male-dominated courses

I'm teaching a graduate applied mathematics qualifying exam review course this summer, and I have 9 males and 1 female. My co-instructor and I are also both male. While I don't necessarily see this ...
icurays1's user avatar
  • 485
13 votes
1 answer
214 views

Question about the process of creation of problems and exercises in Mathematics

I have a question about formulating problems and exercises in Mathematics. When attempting to create a problem of Number Theory or Real Analysis, for example, in this process, is the problem first ...
danilocn94's user avatar
0 votes
2 answers
83 views

Can I do a PhD after many years I've graduated and can I get funding? [closed]

I'm in my second year of Mathematics. I would like to take a PhD and if possible also a master. However, I was thinking to take a master in Machine Learning, work for a bit in that industry (5-10 ...
Euler_Salter's user avatar
11 votes
2 answers
202 views

Transitioning from 'Read textbook to learn' to 'Read original paper/Read paragraphs of textbooks'

I wanted to ask the following on Mathematics stack exchange, but checking the help centre, it appears that this site is more relevant: "Mathematical education, especially about teaching and pedagogy: ...
Display Name's user avatar
14 votes
2 answers
2k views

Does learning classical approach to differential geometry before modern approach help or hinder?

To my mind, there seem to be two main paths to differential geometry. There is the classical approach, focusing on curves and surfaces in $\mathbb{R}^n$, especially $\mathbb{R}^3$. Prerequisites tend ...
J W's user avatar
  • 4,654
9 votes
3 answers
2k views

Mathematics in UK vs Central Europe

Is mathematical education better outside UK and USA? Studying in UK I noticed that the Uk syllabus of 3-4 modules per area of mathematics, is often easily covered by one module in central Europe, for ...
Euler_Salter's user avatar
8 votes
1 answer
113 views

Assessing the level of students in a class

Recently I've moved to another university and next semester I will have my first class there. The problem is that I don't know the level of the students that will be attending my class. Of course, I'...
dtldarek's user avatar
  • 8,947
2 votes
0 answers
126 views

Sketching paraboloids on paper

I have to teach sketching paraboloids on paper by looking at it's equation. Last year when I taught this topic no one was interested in learning this particular thing. They felt the topic difficult ...
Heisenberg's user avatar
6 votes
3 answers
220 views

References for graduate education

A search in Google returns lots of studies and thinkings about teaching in undergraduate schools. Could anybody come up with any research/references about teaching in graduate schools (graduate ...
user avatar
7 votes
1 answer
227 views

The role of visualization and intuition in graduate and postgraduate math and developing it

[I am not an mathematics educator; but because the process of learning is educating yourself, I'm posting it here] In Visual Complex Analysis's preface, the author gives an analogy with pseudo-deaf ...
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