Discrete Mathematics 1

A total of almost 61 hours of lectures

This is the first part of our series of three courses in Discrete Mathematics. It can be seen as a bridging course from high school to university mathematics, as it lays the foundation for all future maths courses, teaches you the basics of mathematical reasoning, and the main proof techniques.

Image precalculus part 1

Prerequisites

High-school maths, mainly arithmetics.

Curriculum

Make sure that you check with your professor what parts of the course you will need for your exam. Such things vary from country to country, from university to university, and they can even vary from year to year at the same university.

Discrete Mathematics 1

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Get the outline

A detailed list of all the lectures in part 1 of the course, including which theorems will be discussed and which problems will be solved. If you are looking for a particular kind of problem or a particular concept, this is where you should look first.

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Course Objectives & Outcomes

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How to solve problems in chosen Discrete-Mathematics topics (illustrated with 395 solved problems) and why these methods work, step by step.
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Elementary Set Theory, including working with intersections and unions of sets, and other set-related topics.
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The concept of function between two discrete sets: injections, surjections, bijections.
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RST relations and the concept of equivalence classes; an illustration for a modulo relation between integers.
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An introduction to the topic of sequences, only basic concepts that can be needed in Combinatorics; we come back to the topic of sequences in DM3.
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A preparation for Combinatorics: the concept of index, the sigma sign (with computational rules), n factorial, n choose k, Pascal’s Triangle, Binomial Theorem.

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Playful logical problems and riddles, including the famous Zebra Puzzle (Einstein’s Riddle), and some classical riddles about liars and truth tellers.

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Elementary Logic, including proving tautologies that involve implications, conjunctions, and disjunctions; necessary and sufficient conditions.
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An introduction to mathematical theories, with concepts like axiom, theorem, primitive notion, etc.

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The concept of (a binary) relation as a subset of Cartesian product of two sets: RST relations, order relations, etc.
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Functions as relations; various ways of depicting functions between two discrete sets; equipotent sets.

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Various proof techniques, including direct proofs, proofs by contradiction, proofs by contrapositive, Mathematical Induction, and Pigeonhole Principle.
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A brief introduction to Combinatorics: the art of counting. Permutations, combinations, paths, etc; the topic will be continued in the first sections of DM2.
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This is the first course in Discrete Mathematics, so don’t worry that neither Number Theory nor Graph Theory are covered; they will be covered in a sequel.
Mervan P.
Udemy student
The most comprehensive , engaging and visually appealing Discrete Mathematics course on the internet. I don't know any other course which is near to this level.

Update 16.08.2025

I almost finished the course, the only final chapter "Proofs" is not yet completed, which is the biggest section in the course and I can safely say that my thoughts stayed the same.

The lecture slides are the backbone of this course and show you diagrammatically how concepts are RELATED to each other, which supports the latest studies regarding effective learning and studying. Our brains almost immediately forget when exposed to complicated formulas, which is the standard in mathematics, but her style of teaching has the complete opposite effect. Thus I strongly recommend anyone who wants to learn DM to take this course, you will not regret it.
K S.
Udemy student
モバイルでは何故か音声が出なかったMachine translation: For some reason, there was no sound on my mobile device.
Andrzej P.
Udemy student
A beautifully structured course, with clear explanations and examples. It is clear that the lecturer is highly experienced and has a deep understanding of the subject.
Varga-Henn M.
Udemy student
Well detailed introduction!
B D.
Udemy student
This is the kind of math course I wish I had a long time ago. Taught from a person who helps you see that math can be fun, interesting and not so mysteriously unreachable after all. I enjoy the pace and great resources, and hearing the instructor Hania speak too. I wish my own school teachers were as calm and engaging.
Kerry W.
Udemy student
She explains everything in a simple and natural way, including the "why" and not just the "how". The pace is such that many students will be able to follow it without any backtracking. She generally keeps the focus on one topic, but sometimes discusses supporting material at just the right time to enhance the learning experience. And, if the student misses something the first time, a second viewing will take care of it. I also appreciate it that she sometimes goes beyond the normal course material and explains concepts that don't usually fall under the description of Discrete Mathematics. Her courses have sufficient substance, while many of the competing courses are much too abbreviated to be of significant value. You cannot learn Discrete Mathematics in twenty lecture hours, unless you already knew most of it.
SHIBAJI M.
Udemy student
The lectures made difficult topics easy to understand
A P.
Udemy student
I am looking forward to doing this course because of the thorough introduction. I am also doing Precalculus 1: Basic Notions. At least, at first I will be concenrrating more on Basic Notions. I am going slowly, however, through Basic Notions because I am trying to do a lot of problems after every section or after a few sections. I am hoping to do all (!) the courses offered and I want to give myself strong foundations.
Łukasz D.
Udemy student
NIc dodać nic ująć.Machine translation: Nothing more, nothing less.
Toby W.
Udemy student
Some of the best explanations I have ever seen and heard. The level of understanding she presented is a plus.
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