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Questions tagged [undergraduate-education]

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

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Difficulty in teaching the coordinates of a vector with respect to a basis $\{v_1,v_2,\ldots,v_n\}$

Let $V$ be a finite dimensional vector space and let $B=\{v_1,v_2,\cdots,v_n\}$ be a basis of $V$. If a vector $v$ can be written as $$v=a_1v_1+a_2v_2+\cdots+a_nv_n,$$ we call $(a_1,a_2,\cdots,a_n)$...
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Studies about group tutoring sessions

I’m not sure if this question belongs here, so I apologize if it doesn’t. I work in a tutoring center at my university where we tutor every subject. Mathematics is in high demand, and occasionally my ...
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5answers
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How does knowing more about mathematics help one's teaching of lower level course, such as calculus?

A question has been asked about why great mathematicians are not necessarily great teachers. On the other hand, I am wondering if knowing more mathematics actually helps with one's teaching of lower ...
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How to deal with a “protest” assignment?

I just received one assignment (by email) from a student. Out of 6 questions, "I don't know" is the answer to 4 of them. There is also a comment at the end of the assignment which suggests my ...
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3answers
130 views

Calculus workbook suggestions

Context: I am an assistant professor of mathematics at a small institution in the US. Our department uses Stewart's Essential Calculus for our calculus sequence, but I find that my students and I are ...
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213 views

Book recommendations on mathematics education focusing on geometry

I will be teaching Euclidean geometry to future teachers, and I am feeling a bit lost (I know geometry, but I am not that familiar with mathematics education). Is there some recent (as concise as ...
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Is it a problem if a senior student majoring in mathematics could not prove the quadratic formula?

According to a recent experiment conducted by user Steven Gubkin, nearly one half of his students in a senior level Real Analysis course do not have any idea how to prove the quadratic formula. Is ...
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131 views

What is a good format of tutorial sessions?

At my university, traditionally a few lectures of a course should be tutorial sessions. The idea is that instead of covering new materials, the teacher should go over many exercises so that student ...
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2answers
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Published papers for Intro Stat students to read

I am looking for studies and experiments in the literature that I can share with undergraduate students in an intro statistics course. I do not expect students to understand everything, and I plan to ...
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1answer
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How to balance the difficulty level and speed of lectures for students of very different levels?

I noticed that in my undergraduate class a few students understand things quite fast and some times see the proof before I even explain things. But some of them also have trouble understanding quite ...
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2answers
117 views

How to explain linear approximation to an equation to calculus students?

I am, at the moment, teaching calculus to students whose majors are, for example, biology, biochemistry, chemistry and geology. The course book is Claudia Neuhauser's "Calculus for biology and ...
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2answers
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Is there any alignment on what a maths grad should know?

This more specific question relates to a more general question of what is a maths degree aiming for. Do any universities define a high level goal for pure mathematics degrees at all? If so, are there ...
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Are students majoring in pure mathematics expected to know classical results in mathematics very well by their graduation?

For example, I am confident that very few students majoring in pure mathematics can write a complete proof to the Abel–Ruffini theorem (there is no algebraic solution to general polynomial equations ...
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2answers
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Vector calculus texts that are free-as-in-speech?

I'm looking around for a text that covers vector calculus and multivariable calculus, and that is also "free as in speech," not just "free as in beer." In other words, I'm looking for texts that are ...
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Tactile Learning Activities in Mathematics

Julie Barnes, Jessica M. Libertini. Tactile Learning Activities in Mathematics: A Recipe Book for the Undergraduate Classroom. 2018. MAA Press. AMS Bookstore link. Can anyone comment / review ...
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Should theorems be proved to students who are not majoring in mathematics?

My impression to students majoring in mathematics is, whenever we teach them a theorem, a proof should be given in the class, or at least as a reading assignment. However, how about students not ...
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Long-form, multi-step, skills-integrating applied mathematics problems in calculus I, II, III

When recently teaching Calculus II to college students, I instructed my students to read and be ready to work through the first 8 or so questions of James Walsh's climate modeling differential ...
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4answers
281 views

How to deal with students who object to me teaching material that won't be in the exam?

I sometimes encounter students who ask questions like 'Why are we learning this if it won't be on the exam?' If there is time to spare I like to teach interesting applications or natural extensions of ...
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1answer
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Measure of Improvement in Math Skills from Remediation with ALEKS

I am analyzing some data on ALEKS for my home institution (ALEKS, an acronym that stands for "Assessment and Learning in Knowledge Spaces", is an online tutoring and assessment program that includes ...
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3answers
179 views

Recommended list of things calculus students should be required to memorise?

I am seeking a list of topics that students taking calculus should memorise. Some topics from Calculus I might include: $\varepsilon-\delta$ definition of limit; Definition of the derivative of a ...
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1answer
130 views

Grades in a university course on category theory, curving, and how they reflect on the students and/or teacher [closed]

I originally posted this on the Mathematics Stack Exchange, thinking that the best place to post it, but the question quickly accumulated a bunch of close votes since it was not quite within the scope ...
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2answers
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Quadratic modeling project with upward-facing parabola

I'm teaching a college algebra course and I'm trying to design a few projects that involve modeling with quadratic functions. So far I have two ideas that involve downward-facing parabolas (projectile ...
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2answers
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A Markov chain demonstration that doesn't require computers

I have a large probability class and would like to do some memorable demonstrations of Markov chains for them. Does anyone have any recommendations for a "low-tech" demo that doesn't involve ...
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1answer
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When self teaching, should I learn set theory before continuing ap calculus?

I am studying ap calculus now, before I move onto differential equations etc., but the thing I am unsure of is, should I learn set theory before continuing on my ap calculus sections?
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In which course should we teach solving general cubic and quartic equations?

I am guessing solving general cubic and quartic equations should be taught in a course somewhere between precalculus and Galois theory, though personally I do not recall learning this topic ever in ...
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2answers
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Topics in Mathematics for a 15 minute demonstration

I need to appear for an interview for the post of Assistant Professor in Mathematics in an undergraduate college. My Backgorund : I have studied topics like Algebra comprising of Group Theory,Ring ...
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3answers
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Is it a bad idea to use an old textbook such as Differential and integral calculus, with examples and applications for calculus course?

I am wondering if it is a bad idea to use an old textbook, such as Differential and integral calculus, with examples and applications by George A. Osborne. This book was published in 1906 and there ...
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3answers
158 views

How to introduce Group Theory to a general audience in 15 minutes?

How to introduce Group Theory to a general audience in 15 minutes? I know that it will be quite tough to introduce Groups to a general audience in such a short time. So what will be a good way to ...
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3answers
225 views

Formats for Calculus instruction at different colleges and universities

In the comments under another question, a couple of people expressed interest in how Calculus is taught at the University of Michigan. I'm not convinced a question that narrow is appropriate for this ...
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2answers
95 views

Returning Student for STEM - Brush-Up Resources? [closed]

All, I am hoping to wade into an Electrical Engineering or Mechanical Engineering degree, but I have been out of college for almost 10 years. My last major exposure to math was good grades in ...
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0answers
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Is it the college teacher's responsibility to help the struggling students? [closed]

I understand that at high school level or below, teachers usually spend extra effort helping those students who are struggling. However, how about at college/university level? Here are two ...
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1answer
143 views

Flipped introductory real analysis resources?

I am going to teach a flipped real analysis class next term, using Abbott's book. Does anyone know of resources for such a class? I have found the article: "Flipping the Analysis Classroom" by ...
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1answer
95 views

Accessible written proof of the Nash Indifference Theorem (game theory)?

In game theory, the Nash Indifference Theorem states that if a mixed strategy $A$ is a best response to a mixed strategy $B$, then every pure strategy in the support of $A$ is also a best response to $...
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6answers
363 views

How to make students understand/remember that $x^2 = a$ has two solutions?

I teach math in university, in France. This semester I have first-year bachelor students. I am becoming increasingly annoyed that they cannot remember the simple fact that $x^2 = a$ has two solutions ...
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Formal linear combinations: motivating examples

I want to introduce formal linear combinations in an upper-level undergraduate combinatorics class. By this I mean expressions like $7 \operatorname{cat} + 5 \operatorname{dog} - \sqrt{2} \...
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4answers
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Beyond cubic polynomials: Applications?

Cubic polynomials are crucially important in computer graphics: for example, cubic Bézier curves/surfaces, and cubic splines, which have many practical applications. Essentially visual continuity ...
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Succinct description of situations where naively obvious is correct, but for far more complicated reasons?

What is the name for a situation where the obvious thing turns out to be true, but the reasoning is more complicated? In abstract algebra we can say the rational numbers - the fractions, $\mathbb{Q}...
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1answer
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Is it feasible to expose undergraduates to a “map”-centric point of view early on?

Question: Would it be feasible to teach undergraduate math students a "map"-centric view early on? If so, how early on? Now that I'm preparing for a phd program, I'm also reflecting on my ...
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2answers
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How is it correct for a lecturer to prove and “explain” a proof while explicitly knowing students are not familiar with logic itself?

I often see a situation when professors use words "logic", "mathematical proof" and even prove logically while actually knowing that students are not even familiar with logic itself, i.e. no formal ...
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I’m considering buying Art of Problem Solving. For those who read it, what’s your review of it? [closed]

As you know, Art of Problem Solving includes 11 books that comes with their solutions and they are PreAlgebra, Introduction to Algebra, Introduction to Counting and Probability, Introduction to ...
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1answer
101 views

A robot to simulate differential equations for undergraduate students. [closed]

I was recently at EPFL drone days and enjoyed a demo of a robot that could follow a black line like in the sketch (I can improve the sketch on demand): Then I remembered my good all times at the ...
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4answers
167 views

Automatically creating homework worksheets from textbook problems

This semester I am a TA for a Calc 2 course. At my first meeting with my instructor, he mentioned in passing that "Homework is always easier than an exam, because homework questions come from the ...
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1answer
107 views

Pythagorean triples

What is the most motivating way to introduct Pythagorean triples to undergraduate students? I am looking for an approach that will have an impact. Good interesting or real life examples will help. Is ...
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0answers
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How to create educational linear algebra animations?

I'm looking to create animations for a linear algebra course. I need things like writing and changing equations, including matrices, plotting of 2- and 3-dimensional axes with points, vectors, lines ...
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3answers
196 views

What is the best way to assign letter grades in a math class?

Here's the most common way that I've seen letter grades assigned in undergrad math courses. At the end of the semester, the professor: 1) computes the raw score (based on homework, quizzes, and tests) ...
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1answer
105 views

Why emphasize moment generating function over characteristic function in a probability course?

I've noticed that some undergraduate introductory probability textbooks and courses emphasize or seem to prefer the moment generating function $m(t) = \mathbf E(e^{tX})$ of a random variable $X$ ...
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4answers
166 views

What are standard (or good) textbooks for undergraduate graph theory?

I'll be teaching graph theory this fall for the first time. The only undergraduate graph theory book I am familiar with is Doug West's book, which I like. But I'd like to consult some other ...
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2answers
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Why are proofs written in flowery language incomprehensible?

Let's take an example in Wu-Ki Tung, Group theory in physics: Theorem 3.4: Irreducible representations of any abelian group must be of dimension one. Proof: Let $U(G)$ be an irreducible ...
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1answer
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Polar form before Cartesian form when introducing complex numbers

When I teach complex numbers to undergraduate engineering students, I invariably start, as appears to be customary, with $a + bi$ (or $a + bj$ for electrical engineers) and then follow up with the ...
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Learning math historically

What is meant by learning math historically (NOT learning math history only, but learning math with a historical development perspective)? I've seen some sources that to learn a math topic X, you need ...