Questions tagged [undergraduate-education]

For questions about teaching students at the undergraduate (university) level.

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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-...
Uagi's user avatar
  • 63
4 votes
3 answers
419 views

Regarding finding eigenvalues and minimal polynomial of an operator with limited tools while following Sheldon Axler

I am using the textbook Linear Algebra done right by Sheldon Axler (fourth edition) to teach an undergraduate linear algebra course. Please find here a link to the book here. Now Axler does not ...
user534666's user avatar
0 votes
0 answers
81 views

What books does a Chinese institution use in the undergraduate maths courses?

Can anyone share the books that a Chinese maths undergraduate follows during their course? Also what are some of the problem books and exam papers that the Chinese students use to become better in ...
Soumyadip Das's user avatar
7 votes
6 answers
2k views

How can we motivate that Newton's method is useful?

If you teach Newton's method for finding roots of real functions on the high school (or freshmen) level, I think some students may reason like a variant of the following: Why do I need learn such a &...
Julia's user avatar
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11 votes
5 answers
1k views

Textbook For a Course on Classical Geometry

I have been assigned to teach a first year course in geometry the next academic year. This course has been running for quite a while in the university, but of late, has been thought of as redundant ...
Aravind Gundakaram's user avatar
-4 votes
1 answer
234 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 ...
Soumyadip Das's user avatar
5 votes
1 answer
220 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 ...
faceclean's user avatar
  • 771
4 votes
1 answer
361 views

Problem of the Week for College Students

Trinity's Problem of the Week and Purdue's Problem of the Week were both weekly problems that were excellent for college math clubs to tangle with at their weekly meetings. However, both of them are ...
user23487's user avatar
7 votes
7 answers
1k views

Special topics for introductory probability

I am helping to design a low-level college course whose purpose is to teach critical thinking, logic, finance and probability. I have been tasked with developing the probability section. I am ...
dt688's user avatar
  • 173
8 votes
4 answers
3k views

Any examples of calculus sequence that deemphasizes calculation tricks?

I'm considering creating a series of classes that explore deeper ideas in calculus without overemphasizing the various computational tricks used in integration and differentiation. My vision is ...
Bilbo's user avatar
  • 271
2 votes
0 answers
122 views

"Tools" (literarily) for solving linear or quadratic equations

Since a few weeks, I teach as a tutor (not from that school) a support course in a German 9/10 class. I quickly noticed a horrible lack of basics. (Partly based on just different names - I had to ...
Hauke Reddmann's user avatar
9 votes
7 answers
431 views

Loaning students calculators during exams

Context: I am an associate professor at a small liberal arts institution in the US. I find in my introductory business math course that students sometimes fail to buy a calculator for the course, ...
AegisCruiser's user avatar
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7 votes
1 answer
670 views

Bridging the gap between students' intuitive problem-solving abilities and expressing ideas through formal writing

Seeking guidance on how to assist students who possess a solid grasp of problem-solving concepts, allowing them to intuitively arrive at solutions, yet encounter difficulties when it comes to ...
user1258481's user avatar
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 ...
Soumyadip Das's user avatar
0 votes
1 answer
2k views

How does a math Olympian fare in undergraduate maths courses?

I am a maths enthusiast and have been exposed to maths olympiad problems for some time. I wanted to know how does a math Olympian do in undergraduate courses of mathematics, statistics or computer ...
Soumyadip Das's user avatar
6 votes
4 answers
2k views

How can we explain intuitively the convergence and divergence of these two series?

It is known that $\displaystyle\sum_1^{\infty} \frac{1}{n^{1.000001}}$ converges while $\displaystyle\sum_{n\text{ is a prime number}}\frac{1}{n}$ diverges. Though we can logically prove these results,...
Zuriel's user avatar
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1 vote
1 answer
94 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
33 votes
17 answers
7k views

Natural origins or learned habit: Why do students skip concepts before applications?

When teaching elementary mathematics, it takes a lot of time and effort to teach students that our goal is not to learn the examples, but to learn the concepts first, and then apply them to specific ...
Mahdi Majidi-Zolbanin's user avatar
29 votes
3 answers
7k views

When is it appropriate to warn about the difficulty of a subject?

I've been a TA across every class in the calculus sequence, under the assignment of professors with different teaching styles and curricula. It's often clear to me ahead of time when a certain subject ...
Feryll's user avatar
  • 399
24 votes
14 answers
16k 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
15 votes
15 answers
7k views

Students can't seem to grasp the intent of tangent lines and getting general trends of derivatives from graphs

Background I'm informally helping a few students with college Calc 1. This isn't the first time I've aided people with calculus, and so they've sought me for help, though I don't consider myself to ...
Krupip's user avatar
  • 291
1 vote
1 answer
344 views

Is there any university or college in any country where failure and dropout rates in Calculus are not so high?

Calculus is a foundational mathematics course that is often seen as a bottleneck for STEM majors. However, it is also a course that is notorious for its high dropout rates. In the United States, for ...
Humberto José Bortolossi's user avatar
5 votes
1 answer
2k views

In math exams, how rigorous should the questions be?

We have theoretical questions in our exams (often in ABCD format). For example, I can state the question: For an indefinite integral, does it hold that $\int f(g(x)) \cdot g'(x) \, dx = \int f(x) ...
Jake B.'s user avatar
  • 167
6 votes
4 answers
648 views

What mathematical topics are important for succeeding in an undergrad PDE course?

I am a student helping to develop a remedial course for other students who have recently failed the undergraduate PDE course at our university. The topics are provided from the syllabus in the ...
brodybjones's user avatar
2 votes
1 answer
379 views

Sources on inequity in precalculus sequence

I'm trying to put together some thoughts on the importance of a strong college precalculus sequence (mainly I'm thinking College Algebra, where much of my experience is) for addressing socioeconomic ...
TomKern's user avatar
  • 4,022
5 votes
0 answers
168 views

Is it better to teach category theory in the background of type theory than set theory?

I have been going over some applied instances of category theory in Programming, and also by a book by conceptual Mathematics by Lawvrere, and I think an issue of applying category theory to real life,...
tryst with freedom's user avatar
26 votes
14 answers
9k views

How to teach pure mathematics to a well-educated adult who did badly in maths at school

My partner is a PhD student in philosophy and has recently developed a keen interest in learning pure mathematics. I am doing my best to teach her (I'm a pure maths PhD student myself) and it is ...
user829347's user avatar
4 votes
0 answers
102 views

Studies on the effects of using online platforms in teaching mathematics on students' beliefs about mathematics

Are you aware of any research examining the impact of utilizing online platforms in teaching mathematics, on students' beliefs about mathematics? To give you an example of the kind of beliefs that I ...
Mahdi Majidi-Zolbanin's user avatar
7 votes
1 answer
98 views

Joint Teaching of a First Year Engineering Maths Class

My department is considering using more than one lecturer (sequentially, not in parallel) to give lectures in our large first-year classes (e.g. 500 students doing engineering mathematics). In other ...
Gordon Royle's user avatar
4 votes
4 answers
339 views

Good analogies for teaching error correcting codes

I'm trying to find a good real-world analogy (or even good visualization) for teaching about error correcting codes and erasure encodings. The most natural way to talk about it really is in terms of ...
Nate Armstrong's user avatar
19 votes
4 answers
4k views

Why do we teach linear algebra in precalculus classes?

When I took precalculus, we learned about polynomials and how to factor them, we learned about trigonometry and lots of great and useful identities there, and we learned about matrices. They didn't ...
Joel Croteau's user avatar
16 votes
7 answers
5k views

Why don’t we teach a topological view of continuity instead of epsilon-delta?

I would like a critique of this approach to teaching continuity to calculus 1 students. Show them that for an increasing function on (a,b) we have that (a,b) is contained in the set of solutions to $...
user avatar
1 vote
1 answer
59 views

Discrete Probability Modeling with Desmos or Spreadsheets

In my Finite Math course* almost every section includes a part where students have to create a file (from scratch) in Desmos or in Google Sheets. For example, they use Desmos to plot piecewise linear ...
Aeryk's user avatar
  • 8,025
1 vote
0 answers
100 views

simpson paradox in classroom: reports?

he Simpson's Paradox is a statistical phenomenon in which a trend or relationship observed within a dataset disappears or reverses when the dataset is divided into smaller groups. It occurs when a ...
Humberto José Bortolossi's user avatar
5 votes
0 answers
153 views

Comparison of texbook for "how to write proofs"

I posted this question in the math stackexchange https://math.stackexchange.com/questions/4681694/comparison-of-textbooks-on-how-to-write-proofs and one person suggested that I cross-post it here. I'...
underflow's user avatar
  • 151
3 votes
2 answers
189 views

What is a theoretical contribution in mathematics-education research?

I am an early-career mathematics-education researcher. Recently, I received a request for major revisions for a manuscript I had submitted on opportunities to learn provided by undergraduate ...
Paul's user avatar
  • 39
8 votes
4 answers
2k views

Seeking Advice on Allowing Students to Skip a Quiz in Linear Algebra Course

I am currently teaching a linear algebra course at a university and have chosen to assess my students using five quizzes throughout the semester, instead of assigning homework. I have encountered a ...
faceclean's user avatar
  • 771
3 votes
3 answers
340 views

Interpreting the derivative as instantaneous rate of change in real phenomena

When interpreting the meaning of the derivative in real phenomena, it may seem that the interpretation is in conflict with the definition of the derivative itself. The confusion is caused by the units ...
Mahdi Majidi-Zolbanin's user avatar
3 votes
5 answers
674 views

Best category theory textbook for undergraduate students

Title is pretty self explanatory. All recommendations welcome. Comments and answers which reject the premise of the question will be met with eye rolling. If I don't see a good enough answer I'll have ...
cheyne's user avatar
  • 280
14 votes
4 answers
5k views

Parentheses around negative numbers

We teach students that a notation like $$17 - -59$$ is not acceptable or at least not good. Instead we want them to write $$17-(-59)$$ The main reason seems to be that it's more readable if you ...
realGottlob's user avatar
38 votes
14 answers
13k views

How to give exercises when students can use ChatGPT

I tried some math exercises we will give to students and ChatGPT does really well answering these. It excels at proofs and often gives details that were not our the example solution, and makes some ...
allo's user avatar
  • 486
7 votes
1 answer
473 views

Homework in a Flipped Classroom

I'm in the middle of teaching first-semester Calculus where, for the first time, I'm trying to implement a flipped classroom. (Background: Small university in U.S.; Calc 1 for STEM majors, 50 minute ...
Aeryk's user avatar
  • 8,025
1 vote
0 answers
173 views

What to cover on a first ordinary differential equations module?

I will have to teach a first course in differential equations. What should I cover in this module? For example, in most books, have Laplace Transforms which is fine but I would not use LT to solve ...
matqkks's user avatar
  • 1,245
11 votes
4 answers
4k views

Is there a fair way to increase the grade of students who did not do well in exams?

How can I fairly compensate a student who showed passion and dedication for my undergraduate course but performed poorly on the final exam, without unfairly advantaging them over other students? ...
faceclean's user avatar
  • 771
5 votes
0 answers
128 views

Is it possible to learn some basic mathematics using an app?

I am interested in developing an app for students that are starting a grade career involving mathematics. It is a real problem that they start with almost no knowgladge of basic mathematics and there ...
Paula Cardoso's user avatar
11 votes
2 answers
2k views

How do/should administrators estimate the cost of producing an online introductory mathematics class?

With the advent of the Internet administrators used to allocate release time or summer salary for making online course content. The pandemic made a Sal Khan out of most of us and making online content ...
Maesumi's user avatar
  • 1,202
0 votes
1 answer
221 views

How to formalize high-school (Euclidean) geometry?

I have unsuccessfully attempted several times over the years to formalize high-school (Euclidean) geometry, or even a working subset of it. Think very simple, diagramless geometry. The usual two-...
Dan Christensen's user avatar
6 votes
3 answers
3k views

Are there examples of central symmetry, without axial symmetry, in nature?

Examples of axial symmetry abound, but I could not find an example of pure central symmetry (that is, without axial symmetry)! Do you know of any? A butterfly shows axial symmetry, what shows point/...
Maesumi's user avatar
  • 1,202
31 votes
20 answers
8k views

‘Lies to children’ in mathematics and statistics education

In teaching, we sometimes necessarily oversimplify concepts. Terry Pratchett famously referred to this as Lies to children: A lie-to-children is a statement that is false, but which nevertheless ...
Joel Ottar's user avatar
3 votes
2 answers
346 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

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