Questions tagged [undergraduate-education]

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

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0answers
16 views

Is the AMC 10/12 Test the Difference Maker for Top Schools? What do Colleges Look for?

I have a few students that know LaTeX who are very young and are extremely advanced for their age in high school. As a teacher, I feel it is my job to get into some of the top tier schools for math ...
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5answers
3k views

Why is the concept of injective functions difficult for my students?

I was aware that students find the definition of function too abstract and thus find it difficult. However, I thought, once you understand functions, the concept of injective and surjective functions ...
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1answer
116 views

Do people usually teach solving a linear differential equation by inverse operators in an undergraduate course?

For the following linear differential equation $$a_ny^{(n)}+\cdots+a_1y'+a_0y=Q(x),$$ most books teach the method of undetermined coefficients, variation of parameters and Laplace transforms. ...
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1answer
194 views

The dimension theorem and pedagogy

The dimension theorem (the rank-nullity theorem) can be explained in many ways. I consider it as a consequence of the first isomorphism theorem/splitting lemma. When I teach undergrad matrix-theoretic ...
5
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1answer
232 views

How important is it to come up with or learn an elementary solution?

Note: by "elementary" I mean "without using more advanced theory and tools". Students are sometimes required or encouraged to solve very difficult problems using limited number of ...
5
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1answer
284 views

Choice of textbook for an undergraduate abstract algebra course

Currently a 5th year PhD student, and I've been fighting tooth and nail to teach one of our junior-year honors sections in undergraduate algebra next fall (desperately hopeful we'll be able to return ...
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3answers
192 views

Applications of abstract algebra outside of mathematics and suitable textbook

The question What are some good mathematical applications to present in an abstract algebra course? asks about mathematical applications of abstract algebra. What are some applications of abstract ...
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0answers
118 views

Have you ever completely covered every topic in a textbook, and if so, which text?

Over the years of being a student or of being a teacher, it's occurred to me that I've never done every topic in a textbook. If it's a workbook that has a few introductory theory pages and then a few ...
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0answers
81 views

Prerequisites to study Laplace Transform completely?

Hello to all the professors who read this. I'm an electrical engineering undergrad student. I wanted to ask for advice on what I should learn beforehand to fully grasp the Laplace transform. I also ...
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0answers
69 views

Number theory in an introductory course on discrete dynamical systems

Benjamin Hutz, in Chapter 10 of his An Experimental Introduction to Number Theory, allows for the optional inclusion of discrete dynamical systems with a number-theoretic flavor in an undergraduate ...
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1answer
193 views

College undergraduate geometry courses

I am interested in learning how a course in geometry is employed today at undergraduate colleges/universities in the U.S. On the one hand, such a course seems to serve as an optional (rarely required) ...
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Exercises for explaning homothety, homothetic center, similarity on line and plane, free vector and vector space

I need the collection of exercises for such topics as: maps and transformations, composition of maps homothety, rotation homothety, homothetic center similarities of the line and the plane free ...
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2answers
205 views

What are some famous problems, which are not difficult to understand, for senior high school students

I hope I am asking my question in the right forum. I am trying to introduce some mathematical problems (Better to be famous in the math community) to a group of senior high school students with a ...
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Looking for papers with teaching-oriented style

I am looking for papers that have the similar style to Hervé Lehning's 1989 The American Mathematical Monthly article "From Experimentation to Proof" (PDF link via lehning.eu). It's like ...
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4answers
646 views

When does thinking $(-8)^{1/3} = -2$ result in problems for an undergraduates?

In high school we learn that the cube root of $-8$ is $-2$. Much later some of us learn about the single valued natural logarithm of a complex number, and that $w^z = e^{z\cdot Lz(w)}$ when $w$ and $z$...
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1answer
256 views

Where does the compulsive use of three dots come from and should it be discouraged?

There are some students in freshman calculus/even precalculus who compulsively use the three dots $\therefore$ in every single step: https://en.wikipedia.org/wiki/Therefore_sign It's not "wrong&...
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2answers
144 views

Why are “homogeneous differential equations” in the standard ODE curriculum?

Here I mean a differential equation of the form $y'=f(x,y)$ where for some $\alpha$, we have $f(tx,ty)=t^\alpha f(x,y)$ for every $t$. I have no idea why this topic seems to appear in every ODE ...
3
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1answer
431 views

How much literature research should one do when designing a course?

For each mathematical subject on the undergraduate level there are many textbooks, often with quite different approaches to the subject. Some are just concise and rigorous, some focus on examples, ...
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5answers
185 views

Question formats for online tests, to deter cheating

I'm teaching calculus 1 online this term and anticipate being plagued by the perennial problem of cheaters. I have seen suggestions for how to arrange the testing time to accommodate for traditional ...
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3answers
278 views

Transitioning proof based math courses online

I'd love to learn from anyone's recent experiences teaching online proof based math courses, especially those that have a large group of students who will be working asynchronously. My usual proof ...
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2answers
486 views

Fear of notation and hazily-appeared writing in Mathematics

I am looking for literature related to fear of notation in mathematics. It is even heard that the font size and font type make a reader reluctant to study mathematical literature, often lecture notes,...
7
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1answer
251 views

Research for Video Length for Math Videos

I'm looking for any references that exist for what a good video length for an online math class should be. I am aware of these three papers but these are basically only for MOOCs - I'm looking for ...
7
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2answers
409 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 ...
10
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1answer
168 views

What is a good place for teachers to share self-created content?

I am a high school mathematics teacher and I regularly create problems and their solutions for my students. It has always lingered in my mind that this content can also benefit others. What would be a ...
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2answers
136 views

Would it make sense for math courses to be pass/fail?

I have a theory that if standardized grading were abolished for a pass/fail system, people would be more mathematically competent. Bear with me here. With graded homework, especially homeworks that ...
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2answers
391 views

Do you mention the continuity and the differentiability of the empty function

My main question is directly related to the title: "Do you mention that (in its domain) the empty function is everywhere continuous and everywhere discontinuous?" (and a similar question ...
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6answers
1k 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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11answers
4k views

When do college students learn rigorous proofs?

I teach in a regional university. In my department, students take their "proof course" (a course that sole focus on writing proofs) in the third or even fourth year. All the courses before ...
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2answers
322 views

The use of “$\therefore$” and “$\because$”

In schools, many students learn the usage of "$\therefore$" and "$\because$" in proofs. Such three-dot notation are popular in many high-school books and exams, but are almost ...
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4answers
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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6answers
1k views

What are the best practices for giving online tests?

Many of us our coming off our first semester of required-online classes; and at some of our institutions we are preparing for what is most likely a required-online semester in the fall. (That is: The ...
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1answer
340 views

How, now, shall we teach math online?

Now that everyone has had the experience of teaching math in an online/remote/synchronous/asynchronous format, and looking forward to more of this in the Summer and Fall terms, how do we change our ...
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0answers
117 views

How must the “ungrading” idea be adapted to work in a math class?

After seeing no direct responses to this question, I'll instead be more direct myself. Ungrading is a buzzword being tossed about for assessing students' progress without focusing on quantitative ...
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1answer
121 views

Undergraduate Interview Maths Questions [closed]

I am trying to compile a document of preparation questions to use in mock interviews with students applying to study Maths at top UK Universities. I have many questions already, but it is always ...
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2answers
133 views

Teaching Approach at primary, middle and higher level

I would like to have a comparison or a big picture of how and why the approach for teaching math varies from primary (or pre primary) to middle to higher classes. I understand at every level one ...
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4answers
2k views

What will my academic path look like after testing out of high school math classes?

I am currently a 15-year-old in the 9th grade, and I am studying to test out all of my high school math classes, which is something I didn't realize I could do in the 8th grade and would have if I had....
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5answers
4k views

(How) Do American undergraduate math programs teach complex numbers?

What kind of exposure to complex numbers can you expect in mathematics majors at American colleges? I teach at a very large public university. It occurred to me that it is possible to graduate in ...
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1answer
85 views

Ideas and/or references for Projects for a Business Calculus course

I have undertaken the teaching a Business Calculus course for this semester (spring II). The various assesments for the students, include quizzes/hw/midterms/final exams, adjusted with suitable ...
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4answers
224 views

Courses equivalent to College Algebra in other countries?

In USA, there is a course called College Algebra and a course description may look like the following: This course provides students an opportunity to gain algebraic knowledge needed in ...
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2answers
169 views

Has a List of Fundamental Mathematical Skills been compiled?

... in the literature. I an wondering is there a (considered) list of "fundamental mathematical skills". I am not sure can I give a solid definition of "fundamental mathematical skill". What I mean ...
5
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2answers
612 views

Textbooks for an independent study in point-set topology

I am planning to sign up for an undergraduate "course" in point-set topology next semester. It is really an "independent study" in that this course will not have any lectures. It will just have two ...
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2answers
106 views

Multiple extra credit questions in a homework set

Extra credit questions sometimes motivate students to study more. Occasionally I find several valuable questions which are all good as extra credit question choices but I have to limit the number of ...
5
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1answer
127 views

Resources for improving computational skills at the high school/university transition

Teaching first year undergraduates, I've noticed that what gives them the most trouble is simple computations like factoring, expanding, handling fractions, powers, especially when variables and other ...
5
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2answers
398 views

Mathematics minor requirements

My institution (in USA) is planning to introduce a minor in mathematics and here are the proposed course requirements: Calculus I Calculus II Calculus III or Differential Equations Any two of the ...
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11answers
4k views

Ideas for explaining 4D and higher dimensions

I introduced the hypercube (to undergraduate students in the U.S.) in the context of generalizations of the Platonic solids, explained its structure, showed it rotating. I mentioned Alicia Stott, who ...
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9answers
3k views

What is the best way to intuitively explain the relationship between the derivative and the integral?

This is my first post so bear with me, but something I've been thinking about lately is: Why didn't I ever question the relationship between the derivative and the integral when I was taking calculus? ...
3
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3answers
894 views

How much does it cost to develop an online course?

Due to the coronavirus outbreak, and other local problems, we are seeing the need of developing most of our teaching online. Just "do a class like always" (but with no blackboard) via some network ...
8
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1answer
311 views

How to conduct online testing for Calculus?

Due to COVID-19, I have been planning to transition to online teaching (which, of course, includes online testing as well). The LMS that we use is Blackboard which is integrated with Proctorio. ...
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2answers
120 views

Topics for undergraduate seminar for mathematics educators

There are some general questions about potential topics for undergraduate seminars: topics for an undergraduate Math seminar Undergraduate Math Seminar topic I am looking for topics for a 15-hour ...
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0answers
170 views

Tablet whiteboard app w e-pencil

(I've generalized the original question as @BrendanW.Sullivan suggests.) I would appreciate recommendations for a whiteboard app for a tablet using an e-pencil. For me: an iPad, using an Apple pencil....

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