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### Calculus problems arising from real research problems

I am visiting my in-laws for the holidays. My sister in law is a statistician. She asked me to take a stab at a calculus problem which was coming up in her research. The Lambert $W_0$ function is ...
• 22.9k
171 views

### Ball rolling down curve simulator

I am preparing a seminar on mathematical discovery for beginner's students, and one of the topics I plan to cover is the brachistocronic/tautochronic curve. For this purpose, I would like to let the ...
• 183
282 views

### Seeking references for why it is good that students understand why mathematical rules work

I am currently advising a student at his final project (it is a graduation course for people who will become math teachers). We've chosen to pick some basic mathematical rules which are (or at least ...
96 views

### Research into the mathematical education of adults with no prior formal mathematical experience

I am curious about the experiences of people who had no formal mathematical training in their youth, but learned mathematics as adults. I imagine that there are a fair number of people in the US who ...
• 22.9k
423 views

### How to explain to undergraduate students what research means?

Background: I am a lecturer in computer science, but my research is mostly theoretic and mathematic, so I ask here. I want to encourage my undergraduate students to become research students after ...
1 vote
91 views

### What are some of the struggles that come with teaching introductory formal logic?

I'm currently an undergraduate student who wants to do research on the pedagogy of formal logic. As a result, I wanted to know what are some challenges that instructors (or even students for that ...
2k views

### How to get better at proofs

As an undergrad student of applied mathematics, I have something to say that make's me ashamed of myself. I suck at proving things in mathematics and i know that if I don't get better in doing this ...
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3k views

### What are some of the open problems that can be suitably introduced in a calculus course?

I feel it may be a good idea to introduce some related open problems in a calculus course. Surely I am not expecting my students to solve any one of them, though I cannot say it is absolutely ...
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526 views

### Grad school after doing an online bachelor's degree without support for undergraduate research

[I originally posted this is the Mathematics Stack Exchange and was told to post it here instead] This might seem like an odd topic for this forum, but I'm losing my mind. I am about eight months away ...
474 views

### Doing research projects when one's knowledge is limited: is it preferable?

In some universities, high schools, and summer programs, students are required to do their own research project in maths and write their own essays/research papers. At the same time, however, many ...
• 1,635
1 vote
295 views

### How to improve mathematical skills(University level)?

I am doing Ph.D in Mathematics, I feel I lack few of the skills, if I can improve those skills I think I can do better as a Math scholar. I need some suggestion on these following(below I am talking ...
• 123
616 views

### Use of Lockhart's *Measurement* in a course?

I greatly admire Paul Lockhart's Measurement (Harvard Press). Many of you know him through A Mathematician's Lament. One review of Measurement said, “Here Lockhart offers the positive side of the ...
• 28.7k
1 vote
114 views

### Subject advice in Number Theory [closed]

At my University, we have the optional feature to write a project like a Bachelor Thesis. This semester have finished and I would like to work in the summer in project like this. So, I'm searching for ...
• 113
300 views

### Can or should students do research in standard major math courses

The following is an expectation for our "course-based research initiative". I'll include the complete wording so you can best understand my question. Designing a Research Proposal/Project ...
• 10.3k
568 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, ...
• 183
69 views

### How to control for numerical factor in mathematics education research?

I am going to carry out a small scale action research on ratio problems. I would ask the same questions in different ways and see whether wordings would affect students' performance. However, past ...
135 views

### Resources for Inquiry-based Projects with Undergraduates

I am teaching an undergraduate course which consists entirely of exploratory projects on any interesting mathematical topic. I'm looking for projects where a first-year student who has only taken ...
• 593
265 views

### Are there any undeveloped areas of mathematics accessible (for both understanding and research) to an undergraduate?

I am a high school senior planning to major in mathematics next year at college. My question is this: Are there any fields of mathematics which do not have a wide body of literature (maybe even just a ...
• 181
177 views

### Catalog of undergraduate's misconceptions / problems while proving

Selden & Selden (2011) listed 41 difficulties their students had in an experimental proving course into 9 categories. Unfortunately I haven't found similar work. Thus, my question is: Is there ...
• 1,991
239 views

### Course-based undergraduate research experiences in math

"Course-based undergraduate research experiences" (CUREs, or CBEs) are being explored in various STEM fields, especially biology, chemistry, geology. Here is one geology link that gives a flavor: "...
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114 views

### Where can I publish on an undergraduate course that I helped develop and teach?

I co-developed and co-taught an interdisciplinary course with several colleagues from several departments for junior/senior college students. This was a very interesting experience, and I am wondering ...
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705 views

### How to prepare for Putnam Competition? [closed]

I am a rising college junior with major in the mathematics. I recently got interested to the contest mathematics through working with few Putnam problems in the real analysis and linear algebra, and ...
• 549
857 views

### Inquiry about My Self-Study Plan for Real Analysis (for my research and self-enrichment)

I am a college sophomore in US with a major in mathematics and an aspiring mathematician in the computation theory and cryptography. I recently got an undergraduate research in the computation theory, ...
• 549
569 views

### Can Compare and Contrast be used in Mathematics Teaching and Research?

I happen to be a fan of the "theme and variations" approach to problem solving. In certain cases, a certain question had drawn enough to attention to generate dozens of solutions. Ways to Prove the ...
• 878
513 views

### Summer opportunities for math undergrads as an alternative to REU

I am currently helping my advisees (undergraduate math majors) plan their summer. As the obvious option, they've already applied to lots of REUs (some have gotten in and others not heard a positive ...
• 413
5k views

### What math courses should be taught to undergrad electrical engineers: a 40 years update

I was browsing IEEE xplore the other day and found this gem called "What Mathematics Courses Should an Electrical Engineer Take? A Report on the National Study of Mathematics Requirements for ...
• 429
195 views

### Learning modulo sticking points, or "fluid study" in mathematics

In graduate school I once tried to rapidly learn mathematics by working through a text and collecting (and precisely remembering) where I had been stuck, and what parts of arguments or computations I ...
• 5,927
272 views

### How to propose subjects for bachelor's theses?

I have recently ended up in a position where I can supervise bachelor's and master's theses, and there has been some discussion in my research group of organizing thesis supervision within the group. ...
• 3,682
673 views

### What does the selection process for counselors at PROMYS involve?

The Information for Counselors page at Promys is not very sapecific: what does one need to do to apply? On which basis are candidates selected? Does anyone have any information from past years (I'm ...
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171 views

I am looking for: an undergraduate research program in mathematics/theoretical physics offered online (e.g. via skype or something) given by a good institution which can be followed while attending ...
• 431
921 views

### Problem of a talented student who doesn't like to solve too much problems

Recently I have been perplexed by a non-mathematical problem. One of my Indian student-friend is preparing for the next year's IMO exam but he says that he doesn't like simply doing hard and ...
188 views

### Peer Review of Mathematical Essays

Background I find that the best way for my mathematical modeling class to understand the modeling process is by having the experience of modeling some real world situation of their group's choosing. ...
137 views

### How to nurture an unprepared student [closed]

What and how much scaffolding is necessary for a motivated undergraduate student who doesn't have the ideal prerequesites for work? This could be for a number of reasons: He didn't realize the ...
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1k views

### Good problems that uncover difficult points in a theory

There is a great quote of Yitz Herstein: The value of a problem is not so much coming up with the answer as in the ideas and attempted ideas it forces on the would-be solver." A number of such ...
• 5,927
164 views

### How does an advisor effectively motivate progress on an independent project?

When an excellent student is working on an honors or independent study project, the advisor's job is to not only serve as the content expert, but also to motivate the student to complete the project. ...
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982 views

### How to nurture a good student?

When you encounter a very bright student in a first-year (college/university) class (and who is therefore bored), what do you do? Leaving them to their own devices can be problematic. It can lead to ...
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501 views

### Examples of Research Level Math Discoveries Done by Undergraduate Students

A good way for motivating young students in undergraduate level is telling them that you can do great works! Question. What are good examples of research level mathematical discoveries done by ...
222 views

### Can math movies help us in teaching?

There are many cinematic and documentary movies about mathematics and mathematicians in every field of mathematics. Particularly in logic, set theory and philosophy of mathematics, which are my ...
867 views

### What do mathematicians call a proof?

In mathematics education, "proof" is widely used for many kinds of argumentation. For instance, one example could be called a proof, if it is paradigmatic in the following sense: The argument can ...
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