# Questions tagged [discrete-math]

For questions about discrete mathematical structures and applying to courses with the title "Discrete Mathematics" or equivalent. Since this tag is fairly broad, consider using a more specific tag if appropriate.

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1answer
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### simple statistics (binomial) terminology

Say I have the problem: I roll a die three times and I am interested in the probability of ending up with two 1's. My impression is that a single roll is called a trial. What is the full 3-roll action ...
3answers
229 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, ...
0answers
56 views

### Understanding Modular Arithmetic [closed]

Mathematics Educators. I'm having a difficult time understanding modular arithmetic (particularly its applications for proof writing). I understand very well the basics. I know that $a\equiv b \pmod n$...
2answers
211 views

### Is playing and teaching chess appropriate in private lessons?

I am giving tutoring to a high school student since more than one year and half. He is about 17 years old. He has excellent results in mathematics, being best student in his class for the last year ...
1answer
119 views

### Mnemonics to correlate the definition of “asymmetric relation” and “antisymmetric relation” with the terms [closed]

The definitions from Kenneth Rosen textbook are as : A relation $R$ on a set $A$ such that for all $a,b ∈ A$ ,if $(a,b) ∈ R$ and $(b,a) ∈ R$,then $a=b$ is called antisymmetric. A relation $R$ on a ...
0answers
87 views

### Which resource(s) to use to learn the following syllabus of discrete structures?

(YES) - included; (NO) - explicitly excluded; as stated from the IOI syllabus(2019); 5.2 Discrete Structures (DS) DS1. Functions, relations, and sets (YES)Functions (surjections, injections, inverses, ...
2answers
259 views

### Is there any example of a “forwards/backwards” induction?

I like to make the "dominoes" analogy when I teach my students induction. I recently came across the following video: https://www.youtube.com/watch?v=-BTWiZ7CYoI In this video, a sequence of ...
2answers
149 views

### How to summarize textbook material?

I'm taking a discrete math course. The textbook we use is such a pain to read because the amount of material is very overwhelming. For example, chapter 1 alone is 115 pages. And every subsection, 1.1-...
1answer
202 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) ...
14answers
4k views

### What's the point of learning equivalence relations?

I teach an introductory discrete mathematics course at a community college to math and computing majors, usually in their sophomore year. As is common, it's partly used as the first foray into formal ...
4answers
285 views

### Textbook to study group theory as a part of Discrete Mathematics

I am a student from CS background. I have been following "Discrete Mathematics and its Applications" by Kenneth Rosen, though it is a good book, but it does not cover group theory. I would like to ...
2answers
87 views

### Need to learn recurrence relation discrete mathematics [closed]

Which is the best tutorial available online to learn the recurrence relation concept and its solution in discrete mathematics, in a systematic way?
2answers
752 views

### Emphasizing the discrete in early undergraduate education?

From time to time, I have come across course ideas emphasizing the discrete over the continuous, such as Peter Saveliev's Fantasy Math curriculum (update: see also his material on discrete calculus) ...
2answers
429 views

### Teaching logic through “high school algebra”?

I am going to be teaching a discrete math class in the fall. One of the major goals of the course is a solid understanding of the basics of logic: the precise meanings of "and", "or", "not", "implies"...
2answers
224 views

### Are there mathematical proof info-graphics?

I am teaching mathematical proof to kids (10th grade) and am of the opinion that proofs of theorems are a good place to start, where almost all of mathematics' important players come together. On ...
4answers
799 views

### Proofs that make theorems less clear

Teaching Theory of Computation for the first time, I encountered a phenomenon which perhaps is familiar to others in different contexts. I realize most MESE participants are not conversant with Th....
1answer
180 views

### What is the best way of introducing set theory? [closed]

The students are aware of mathematical logic and proof but have not come across any of the notions of a set. What is the most natural and motivating way to introduce set theory?
3answers
210 views

### Easy tool to draw stencils

I'm looking for a simple tool (preferably online or at least that works on Linux) to draw stencils. When teaching and creating notes for students, I often feel that it would make understanding in some ...
4answers
888 views

### Is Calculus Necessary?

That title is a quote from Fred Roberts: Fred Roberts. "Is Calculus Necessary?" Proceedings of the Fourth International Congress on Mathematical Education. 1980. p.52ff. "Calculus is not ...
0answers
117 views

### Questions similar to Wason Selection Task

The Wason Selection Task (described by Pete Clark here) is a great problem for getting students to grapple with all of the intricacies of logical implication. I will be teaching a discrete ...
4answers
180 views

### Recommendations for free, basic resource on discrete probability for a discrete structures class?

I'm teaching a course this fall on Discrete Structures for Computer Science. It's taught out of the math department but is a service course for the CS department with 90-95% of students being CS ...
1answer
184 views

### Tutoring Discrete Mathematics

A few weeks ago, I started tutoring a student in Discrete Mathematics (a subject I took a year ago). I have previously tutored both pre-calculus and calculus, but never a proof based class. I have ...
0answers
198 views

### Introduction of the power set as a collection of *labels* or *names* for subsets

The way that naïve set theory is usually presented in undergraduate education is via very concrete examples of sets, often involving non-mathematical elements. When power sets are treated, having a ...
0answers
78 views

### Solvability of Systems of Diophantine Equations using Modular Reasoning

I'll be teaching a U.S. college, freshman-level, pre-proofs discrete math course (for future teachers) this semester and one of the topics I like to cover is determining if a system of (usually linear)...
5answers
293 views

### Different approaches to proofs that “are the same”?

This question (and answers) on MSE got me thinking on simple examples of different ways of proving the same (hopefully somewhat interesting) result, as examples to be discussed on difference in ...
2answers
4k views

### Counterexamples to the Greedy Algorithm

In the graph theory section of my Discrete Math course I'll be covering Prim's Algorithm for finding the minimal spanning tree. I'd like to impress upon the students just how special it is that the ...
0answers
147 views

### Why is combinatorics not a part of the Tripos?

I do not officially study mathematics, so I always rely on what's on the internet. Specifically, I follow the schedules of the Tripos – the math program at Cambridge, supposedly one of the most ...
3answers
302 views

### Discrete Math text before a proof course

Our department has decided to offer a "Discrete Math" course that students would take before their "Intro to Proofs" course. The idea is that the Discrete Math course would focus on the computations ...