Questions tagged [undergraduate-education]

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

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8
votes
2answers
355 views

Should we assess ability to use specific problem solving methods, or general ability to solve problems?

This is my first semester being an instructor of record for a college algebra course. One of the sections we cover is "methods of solving quadratic equations", where we discuss factoring and ...
7
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3answers
383 views

Resources for mathematics for sustainability

I am looking for resources (books, websites, etc.) for mathematics relevant to or in the context of sustainability, broadly construed, at upper secondary or early undergraduate level - so not ...
2
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1answer
131 views

How can maths assistants at a college be extra helpful for professors?

I am a maths graduate student. A little background: In the coming semester, I will be assisting a prof whom I admire and whom I also want to thank a lot, and I actually will have a lot of free time. ...
1
vote
2answers
221 views

Real before complex analysis or vice versa?

I used to learn Real Analysis before Complex Analysis in my bachelor study, but now the order is reversed in my university. I would like to ask which order is better to learn the subjects, and which ...
6
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5answers
676 views

Does the way we often introduce the concept of a function make sense?

Here are some ideas and a few questions I've been pondering lately related to the teaching of functions in college algebra and precalculus: Based on my experience, the teaching of functions usually ...
5
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2answers
379 views

Undergraduate-level abstract algebra books or courses that don't start with groups or rings

When I was an undergrad studying abstract algebra, we used the second edition of Artin and covered groups first and then rings. Fields, vector spaces, and algebras came later, I think. I remember ...
5
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4answers
687 views

Teaching Mathematics to a Machine Learning Class

How and what mathematics must be taught for training engineering students with the mathematics required for Machine Learning? How can one conduct training of mathematics required for application-...
6
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5answers
1k views

How do math professors select textbooks?

I will describe what I mean by the above with an example. Suppose you are a professor, about to teach a first Calculus course in a university. There are dozens, if not hundreds, of calculus books out ...
4
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2answers
106 views

Textbooks with solutions and catering to different circumstances

Questions: Are we really taking students into account FULLY when writing textbooks for various areas? Also, are we being unintentionally elitist or dismissive when neglecting to take a more humble ...
6
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3answers
306 views

Is there a study that compares 8-week vs 16-week math classes?

I see a push toward having undergraduate curriculums built around 8-week classes. This is mostly in the online education in the USA. Recently I have seen a number of these in sophomore or junior-level ...
4
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2answers
195 views

Are there any list of mathematical constructions which can challenge 12-16 year old students?

Mathematical (geometric) constructions are an interesting way to engage students. It also helps in better understanding of different geometrical properties. For example, Sierpinski triangle or square, ...
2
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3answers
193 views

If one wants to conduct a 1/2 day workshop in Mathematics for 12-16 year old students - how one should go about preparing the workshop

The questions that I want ask are the following: What are the most important and effective topics to conduct a workshop? What fraction of workshop should include lectures, activity, problem solving, ...
2
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1answer
195 views

How to teach if calculations and algebraic manipulations are off limits

This question may be just too broad in scope, but some form of it has been on my mind during this year of remote learning as I imagine a future cycle of educational upheaval. Much of what we teach in ...
4
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0answers
83 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
362 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
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2answers
201 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
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1answer
145 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
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2answers
165 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
117 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
424 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
896 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
201 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
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3answers
234 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
241 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
246 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
151 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
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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
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2answers
182 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
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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
331 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
265 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
279 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
330 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
208 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
123 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. ...
7
votes
1answer
226 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
252 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
434 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
233 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
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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
101 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
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0answers
75 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
209 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
43 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
244 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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