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29 votes
Accepted

What's the point of learning equivalence relations?

Perhaps emphasize to students the spirit of equivalence relations. They partitions sets into equivalence classes--cutting down the amount of cases necessary to prove something. To illustrate this, ...
Andrew Sansom's user avatar
27 votes
Accepted

What are some rationales to teach Computer Science students Sequences and Series?

Big O and related notations relate closely to these notions. They are often defined using limits. Although it is also possible to define them without using limits, the style of those definitions is ...
dfsjkhsldfkh's user avatar
23 votes

What's the most practical and efficient way to sort exams on paper?

An eminently pragmatic question about sorting! :) When I was dealing with 150+ papers, on a not-too-large table-top, after various experiments, I found that subsets of 10 or 12 I could visually sort ...
paul garrett's user avatar
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16 votes

What's the point of learning equivalence relations?

In general, all applications are going to be more of the "here is what we have to check to make sure that our algorithm/theory/definitions work". We don't usually encounter practical ...
Misha Lavrov's user avatar
16 votes

Should mathematical logic be included in a discrete mathematics course for computer science?

The Association for Computing Machinery (which is the professional association for computer scientists) puts out a curriculum guideline for computer science. While the guideline is for what an entire ...
Alexander Woo's user avatar
15 votes
Accepted

Should mathematical logic be included in a discrete mathematics course for computer science?

Certainly the rudiments of logic are needed in computer science: Enough to understand Boolean expressions in if-statements. if (a < pi) and (not finished), etc. ...
Joseph O'Rourke's user avatar
12 votes

What's the most practical and efficient way to sort exams on paper?

For hundreds of exams, I'm a fan of your second proposed approach, specifically, break up the alphabet into $n$ intervals where $n$ is the number of piles you can reach simultaneously without moving, ...
TomKern's user avatar
  • 4,425
11 votes

What's the point of learning equivalence relations?

Equality vs. Identity Alexei touched on this topic by mentioning hash tables, but I would like to spell it out more explicitly, because this is a critical and fundamental topic in software engineering,...
Lawnmower Man's user avatar
11 votes

Should mathematical logic be included in a discrete mathematics course for computer science?

This is standard in the Discrete Mathematics course. I teach it, and all of the published textbooks I've looked at start similarly with the unit on logic. A few points on this: I mean, you need that ...
Daniel R. Collins's user avatar
10 votes

What should I learn after calculus?

Take your time Andrew, don't worry so much about classes. Learn Python and solve your calculus problems with it. Learn R and solve your Stats problems with it. If you can do this by the end of your ...
jfkoehler's user avatar
  • 1,014
10 votes
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How can I help/tutor a friend who is taking the same course as me?

I had two goals the whole time: do the homework as quickly as I could do it well, and teach him the concepts. If you really want to help, the first goal should be scrapped entirely, IMHO. The best ...
fedja's user avatar
  • 3,939
7 votes

What are some rationales to teach Computer Science students Sequences and Series?

Look at the book “Concrete Mathematics” by Graham, Knuth, and Patashnik, which was written for a course for CS students. Power series show up in the context of generating functions. I think that list ...
KCd's user avatar
  • 3,536
7 votes

What's the most practical and efficient way to sort exams on paper?

Frame Challenge: Don't bother. For the last five or six years, I have been using GradeScope for all of my grading. Before that, I used CrowdMark. Both of these services allow you to upload unsorted ...
Xander Henderson's user avatar
  • 8,225
6 votes

What's the point of learning equivalence relations?

The notion of equivalence relation is one of the basic building blocks out of which all mathematical thought is constructed. (Paul Halmos) What's the point of learning equivalence relations? The ...
Pedro's user avatar
  • 1,800
6 votes

What's the point of learning equivalence relations?

If you have looked at modular arithmetic, then one possibility is: Give/recall some example of an algebraic argument in modular arithmetic; then point out that the argument is implicitly relying on ...
Peter LeFanu Lumsdaine's user avatar
6 votes

Should mathematical logic be included in a discrete mathematics course for computer science?

Senior computer science student here (graduating in December). I took a similar course titled "Discrete Math for Computing" in my freshman year. It's been a few years so my memory is hazy (...
jcgoble3's user avatar
  • 161
5 votes

What's the point of learning equivalence relations?

Dictionary/hash table relies on equivalence to bucketize items. So knowing that one would never try to build a hashtable by a distance between cities (objects on a plane): distance is not transitive. ...
Alexei Levenkov's user avatar
5 votes

Should mathematical logic be included in a discrete mathematics course for computer science?

One very important point to realize is that using FOL is completely different from studying FOL. The first is necessary for all logical reasoning, and hence you should include it in your course, if ...
user21820's user avatar
  • 2,656
5 votes

Should mathematical logic be included in a discrete mathematics course for computer science?

I speak from the perspective of a someone who got a bachelors in CS who is currently teaching a coworker programming. I have no formal training in education. I believe Propositional Logic is essential ...
John's user avatar
  • 151
5 votes

What's the most practical and efficient way to sort exams on paper?

About four times per year, after correcting them, we had to sort 600+ exams by student numbers, which was a 6 digit number given consecutively to all students at enrolment, so kind of the worst case, ...
mlk's user avatar
  • 338
5 votes

What's the most practical and efficient way to sort exams on paper?

I suggest starting with a small table and a large floor area. Sort by the first letter of the name into piles on the floor, grouping rare letters (so at least Q in with P and WXYZ together for ...
Chris H's user avatar
  • 261
4 votes

What should I learn after calculus?

This same question has arisen at my current institution even earlier (i.e., after AP Calculus AB). The traditional next course after the Calculus is Real Analysis (constructing the real numbers in one ...
Benjamin Dickman's user avatar
4 votes
Accepted

How to explain NP-hardness and NP-completeness to students

Admittedly, students will find it easy to believe that computers will take longer to solve a given problem if the input size grows. However, this is also true for problems which can be solved in ...
Kevin's user avatar
  • 586
4 votes

How can I help/tutor a friend who is taking the same course as me?

Although I do think this is appropriate here, it's more a question about interpersonal relationships than about math education. First, what is the problem you want to solve? The only problem you named ...
Sue VanHattum's user avatar
  • 21k
4 votes

What's the most practical and efficient way to sort exams on paper?

I use a set of folders (like this): https://www.amazon.com/Expanding-Multi-Color-Accordion-Organizer-Expandable/dp/B075F1N2DM/ (Can kludge your own also...a milk crate works OK. Or use a filing ...
guest troll luvs alpha org-ing's user avatar
4 votes

What's the most practical and efficient way to sort exams on paper?

I think that Quicksort is very suitable for working by hand. It's reasonably expensive in space (you need a largeish table), but takes only $O(n\log n)$ comparisons on average, which is pretty good. ...
Norman Gray's user avatar
4 votes

What's the most practical and efficient way to sort exams on paper?

For the case when the order key is a natural number: use a jig and a hole punch to punch each paper's key into the top of the paper in binary. Encode a 1 by punching a single hole a short distance ...
hobbs's user avatar
  • 141
3 votes

What's the point of learning equivalence relations?

One of the more popular high-school proofs (Pappus's) that the base angles of an isosceles triangle are equal relies on an equivalence relation. They typically don't call it that in high-school, but ...
RBarryYoung's user avatar
3 votes

Should mathematical logic be included in a discrete mathematics course for computer science?

Practical suggestion: I would doublecheck the rest of the standard curriculum and see if this stuff is covered elsewhere (or a good portion of it). For instance, would be surprised if they are not ...
guest's user avatar
  • 47
3 votes

What's the point of learning equivalence relations?

OP here: There's so many good answers here, this is possibly my favorite question that I've ever asked on SE! I'm so glad that I thought to post the question here. For comparison purposes, having ...
Daniel R. Collins's user avatar

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