Community Digest

Top new questions this week:

Analogies for grad, div, curl, and Laplacian?

I want to try making some calculation-less questions about vector calculus identities that are solely based upon picture diagrams of vector fields, or fields that could be sketched out by hand. The ...

calculus vector-calculus  
asked by Robbie_P_math 8 votes

Is There Such Thing as Reaching Half a Standard?

I like the Common Core State Standards for Math as they focus on objectives that students need to reach. However, some standards have way too many parts for them. For instance, the standard ...

secondary-education common-core  
asked by W. G. 4 votes

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 ...

undergraduate-education proofs undergraduate-research  
asked by Occhima 3 votes
answered by amWhy 7 votes

Logic and proofs in secondary school

Inspired by the question When do college students learn rigorous proofs?, I became curious when pupils in secondary schools learn about proofs, what kinds of proofs they are, how rigorously they are ...

secondary-education mathematical-pedagogy proofs logic middle-school  
asked by Rusty Core 3 votes
answered by Rusty Core 1 vote

How to naturally encounter the properties of identity, commutativity, associativity, and distributivity (to define rings)?

(Cross posted at MSE: https://math.stackexchange.com/questions/3742948/how-did-we-isolate-the-properties-of-identity-commutativity-associativity-and) In elementary school, I remember learning about ...

abstract-algebra intuition arithmetic-operations  
asked by D.R 2 votes
answered by Chris Cunningham 4 votes

Do you mention that the empty function is a continuous and differentiable function?

My main question is directly related to the title: "Do you mention that the empty function is a continuous and differentiable function?" A secondary question I'd ask is, "do you mention ...

undergraduate-education calculus  
asked by Robbie_P_math 1 vote
answered by Steven Gubkin 3 votes

Reference Request: Suitability of a text and corresponding video lecture series request for "Matroid Theory"

I am an undergraduate student from the CS background. While reading a portion of the text "Introduction to Algorithms" by Cormen et. al. I came across a section of Matroids. I was unable to ...

reference-request textbooks  
asked by Abhishek Ghosh 1 vote
answered by Joseph O'Rourke 1 vote

Greatest hits from previous weeks:

Math topics that reward going beyond cookbook methods

Students fresh out of high school are often under the impression that mathematics is a discipline based entirely in recognizing the type of problem and applying an algorithm or cookbook method. These ...

precalculus  
asked by Chris Cunningham 32 votes

Learn university maths or train for high school competitions: which is better?

I sometimes see people arguing against concentrating too many resources in high school maths competition (such as IMO) training. Their reasons they give are usually the following: Competitions are a ...

undergraduate-education secondary-education math-contests  
asked by Ma Joad 17 votes
answered by Peter - Reinstate Monica 20 votes

How to help new students accept function notation

I am struggling to help some of my new precalculus students accept function notation -- something new to them this term. I am looking for strategies to help them adopt this new notation. Their main ...

notation precalculus functions  
asked by Nick C 44 votes
answered by Uwe 24 votes

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 ...

undergraduate-education geometry  
asked by Joseph O'Rourke 10 votes
answered by Humberto José Bortolossi 5 votes

How to explain the difference between the fraction a / b and the ratio a : b?

I found it difficult to explain the difference between the fraction a / b and the ratio a : b. This subject is for pupils of grade 5. So is there a real difference between them and how to explain the ...

undergraduate-education primary-education fractions  
asked by Abdallah Abusharekh 14 votes
answered by Burt Furuta -2 votes

topics for an undergraduate Math seminar

What are some good topics for an undergraduate Math seminar? I am looking for topics which are: Approachable for at least second or third year students and beyond (The students have taken all of ...

undergraduate-education presentation seminar  
asked by Tom 14 votes
answered by Anamaki 6 votes

What should be included in a freshman 'Mathematics for computer programmers' course?

Many universities are changing up the way that they teach math service courses. 1-3 semesters of calculus and maybe a course in linear algebra are often included in majors (such as computer science) ...

undergraduate-education course-design curriculum computer-science  
asked by Brian Rushton 46 votes
answered by dtldarek 46 votes
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