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
57 views

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 ...
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0answers
54 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 $a\equiv b \pmod n$...
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3answers
227 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, ...
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2answers
210 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 ...
1
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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 ...
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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, ...
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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-...
9
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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) ...
28
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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 ...
3
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4answers
283 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 ...
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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?
5
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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 ...
-2
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1answer
178 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?
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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 ...
12
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2answers
427 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"...
2
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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 ...
6
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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 ...
5
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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 ...
2
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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 ...
12
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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 ...
5
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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)...
13
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4answers
797 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....
8
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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 ...
6
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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 ...
6
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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 ...
3
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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 ...
10
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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 ...
20
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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) ...