28
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 ...
- 296
27
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, ...
- 495
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 ...
- 811
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 ...
- 2,484
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.
...
- 29.5k
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,...
- 653
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 ...
- 24.3k
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 ...
- 984
10
votes
Accepted
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 ...
- 3,599
8
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 ...
- 3,258
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 ...
- 1,112
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 ...
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 (...
- 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.
...
- 151
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 ...
- 2,567
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 ...
- 151
4
votes
Accepted
How to motivate 'Theory of Computation'?
They need at least a passing acquaintance with both aspects. There are many practical uses (regular expressions for patterns, context free grammars revolutionized programming languages in ways that ...
- 12.3k
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 ...
- 18.4k
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 ...
- 556
4
votes
What are some rationales to teach Computer Science students Sequences and Series?
Because every single one of those concepts naturally come up when you want to "do" things with computers!
Let make take for example convergent sequences, what does it mean to converge? If we ...
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 ...
- 20.1k
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 ...
- 181
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 ...
- 24.3k
3
votes
When are arithmetic operator priorities typically taught in school, in relation to computer programming?
One data point here ... order of operations, 5th grade (age approx 11). I don't know what (if any) programming instruction occurs by that age.
- 7,369
3
votes
Need to learn recurrence relation discrete mathematics
I liked this Discrete Mathematics: An Open Introduction, by Oscar Levin, for generating functions, so I'm guessing it will be good for recurrence relations.
- 20.1k
3
votes
What should I learn after calculus?
What you likely will not have experienced after Calculus and Statistics is: proofs. At most institutions, both Discrete Math and Linear Algebra introduce, and may even concentrate on, proofs. The same ...
- 29.5k
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 ...
- 47
3
votes
Should mathematical logic be included in a discrete mathematics course for computer science?
The prerequisites of the course are important in recognizing your students' degree of exposure and penetration into these topics. If they've already completed curricula on formal logic and fundamental ...
- 139
3
votes
Should mathematical logic be included in a discrete mathematics course for computer science?
"Discrete Math" is a pretty broad way of categorizing topics in modern mathematics. It was required in my second year of undergrad CS, and mathematical logic was the central theme. We used &...
- 131
3
votes
Should mathematical logic be included in a discrete mathematics course for computer science?
TL;DR: FOL is the Foundation of almost all Information Representation
I'd recommend to include FOL for one more reason:
It's the foundation of nearly all information representation we do in software ...
- 441
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