Questions tagged [undergraduate-education]

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

Filter by
Sorted by
Tagged with
4
votes
0answers
72 views

Objectives for group work in undergraduate pure maths

Whether we are preparing undergraduates for research in industry or academia effective collaboration is an important higher skill. I think there are two aspects to this in mathematics - thinking ...
2
votes
4answers
333 views

Is it necessary to teach the definition of a limit for engineering majors? [closed]

I have always wondered whether it is necessary or not. For me, it seems that it is enough to teach them the intuitive idea, that is, limit is just an approximation of a certain process. what do you ...
3
votes
2answers
187 views

How to make an introductory course on Statistics interesting

I am going to teach this probability and statistics course in a couple of weeks. The probability part can be made very interesting, in my opinion, easily. But I am a little worried that I might make ...
2
votes
1answer
131 views

An intuitive (non rigorous) text book on graph theory which is student friendly with vivid illustrations

Background Hello, I am an undergraduate in CS. I would like to study Graph Theory on my own (self-study) for a competitive examination (named GATE). It is an examination for undergraduates and as such,...
-1
votes
2answers
160 views

What research has been done on the effects of requiring students to learn to count in an alternative number base such a binary or base eight? [closed]

What research has been done on the effects of requiring students to learn to count and do some easy arithmetic in an alternative number base, for example binary, base four, base six, base eight, base ...
5
votes
1answer
111 views

Students reliant on answers provided, but not their own reasoning?

Evidence suggests that even instructional approaches that produce conceptual gains may leave students reliant and expecting to be reliant on guidance from instructors (Redish et al., 1998). Students ...
6
votes
1answer
421 views

“Flipped classroom exercises” resources

I was reading this book: "Dynamics of Particles and Rigid Bodies: A Self-Learning Approach" by Mohammed F. Daqaq In the preface, the author explains of his "flipped classroom ...
7
votes
1answer
884 views

How to be a good math teacher at a liberal art college?

I am thinking of taking up a position at a liberal art college. I have taught mathematics at large public universities but I have no idea what is it like to work at a liberal art colleges. So what are ...
15
votes
2answers
193 views

Tension between the most intuitive definition vs. the most common definition of a concept

Many definitions in mathematics are "fully crystalized". Sometimes the form of these definitions might be somewhat baffling to the uninitiated. For example, the definition of a relation ...
2
votes
3answers
231 views

History of discrete math curriculum

I will be teaching discrete mathematics. I’m wondering if anyone can tell me a couple topics that were classically in this class (in any undergraduate version) that were probably discarded over time, ...
5
votes
3answers
235 views

I need strategies for tutoring a bright, motivated student currently taking college algebra who just doesn't seem to retain the things I teach

I have a college student who I've been tutoring over the past two semesters. He's a hard worker and quite bright. Unfortunately, I do not feel like I am having much success in helping him learn ...
7
votes
3answers
215 views

Rings in parallel with groups in abstract algebra

In a previous question, I asked about the pros and cons of teaching rings before groups in abstract algebra. Recently, it has come to my attention that there is a third approach - a unified approach - ...
2
votes
1answer
148 views

Improving exposition of a proof about polynomials over infinite fields

This question concerns teaching a proof of the theorem that if a polynomial $f \in k[x]$ over an infinite field $k$ is the zero function (i.e. $f(a) = 0$ for all $a \in k$) then it is also the zero ...
19
votes
11answers
5k views

Why do we still teach the determinant formula for cross product? And is it as bad as I think it is?

The cross product is an important vector operation in in any serious multivariable calculus course. In most textbooks that I'm aware of, right after the definition, we always introduce the ...
4
votes
2answers
180 views

Pros/Cons of using a single story in multiple examples to demonstrate different points

Judea Pearl, in his book "Probabilistic reasoning in intelligent systems" uses a handful of stories over and over again, each time to demonstrate a different point. (His "Alarm" ...
8
votes
3answers
253 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 ...
13
votes
3answers
2k views

Finding the Balance in a Math Question (Teaching)

As we try to work and teach in the midst of this pandemic, some problems arise when making online math exams. My question is simple: What could be an interesting basic differentiation question such ...
0
votes
4answers
325 views

Defining mathematics to primary/elementary school teachers

I'm looking for a simple way to define mathematics to primary/elementary school teachers and explain some of the confusion children have. I'm hoping some Algebraist could help me properly state the ...
6
votes
1answer
254 views

Complex analysis books/resources where solutions are difficult to find

I am teaching complex analysis for undergraduates using the textbook Complex Variables and Applications, Brown and Churchill. I am looking for resources that I can use to find good problems for ...
5
votes
2answers
276 views

Curving grades without creating competition among students [closed]

I've recently taken a new position within a math department at a large university. The department has an official policy that in most lower-level undergraduate classes (let's say anything in the ...
2
votes
0answers
74 views

creating an easygoing mathematical course that covers basic concepts that are not in main focus of standard courses [closed]

I want to know which topics should be covered if one wants to create an easygoing mathematical course that covers basic concepts that are not in main focus of standard courses i.e. what those concepts ...
35
votes
6answers
4k views

How can I give feedback that is not demotivating?

Background: To cope with online education, I taught linear algebra using a variant of the flipped classroom. I recorded videos and put them up on YouTube and students presented the content in these ...
7
votes
7answers
1k views

Advice on teaching abstract algebra and logic to high-school students

NOTE: This question will soon be duplicated, as I didn't make clear that I was a high school sophmore in the beginning. At first I thought it didn't matter, and somewhat arrogant to mention, but in ...
10
votes
2answers
320 views

Weekly quizzes as an alternative for midterms? What is this called?

I have seen (by some of my former instructors) the following strategy applied as an alternative to traditional "midterms and final" assessment in a math course: Students take a quiz weekly. ...
2
votes
1answer
190 views

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

The AMC 10/12 test is a test used in a math competition for high school students. I have a few students that know LaTeX who are very young and are extremely advanced for their age in high school. As a ...
20
votes
6answers
4k 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 ...
5
votes
1answer
122 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. ...
6
votes
1answer
216 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
votes
1answer
245 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
votes
1answer
401 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 ...
3
votes
3answers
227 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 ...
0
votes
0answers
125 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 ...
0
votes
0answers
94 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 ...
1
vote
0answers
71 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 ...
9
votes
1answer
204 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) ...
1
vote
0answers
42 views

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 ...
5
votes
2answers
228 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 ...
4
votes
0answers
49 views

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 ...
3
votes
4answers
670 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 $z$...
6
votes
1answer
277 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&...
3
votes
2answers
186 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
votes
1answer
434 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, ...
8
votes
5answers
696 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 ...
8
votes
3answers
323 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 ...
9
votes
2answers
508 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
votes
1answer
253 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
votes
2answers
424 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
votes
1answer
171 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 ...
0
votes
2answers
145 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 ...
2
votes
2answers
428 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 ...

1
2 3 4 5
14