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.
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
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
How to solve problems in chosen Discrete-Mathematics topics (illustrated with 395 solved problems) and why these methods work, step by step.
Elementary Set Theory, including working with intersections and unions of sets, and other set-related topics.
The concept of function between two discrete sets: injections, surjections, bijections.
RST relations and the concept of equivalence classes; an illustration for a modulo relation between integers.
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.
A preparation for Combinatorics: the concept of index, the sigma sign (with computational rules), n factorial, n choose k, Pascal’s Triangle, Binomial Theorem.
Playful logical problems and riddles, including the famous Zebra Puzzle (Einstein’s Riddle), and some classical riddles about liars and truth tellers.
Elementary Logic, including proving tautologies that involve implications, conjunctions, and disjunctions; necessary and sufficient conditions.
An introduction to mathematical theories, with concepts like axiom, theorem, primitive notion, etc.
The concept of (a binary) relation as a subset of Cartesian product of two sets: RST relations, order relations, etc.
Functions as relations; various ways of depicting functions between two discrete sets; equipotent sets.
Various proof techniques, including direct proofs, proofs by contradiction, proofs by contrapositive, Mathematical Induction, and Pigeonhole Principle.
A brief introduction to Combinatorics: the art of counting. Permutations, combinations, paths, etc; the topic will be continued in the first sections of DM2.
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.
Reviews (35)
Hector C.
Udemy student
I love her calm, unhurried voice and the way she teaches with such ease and confidence. She seems completely at home with what she does, like a fish in water. I'll definitely keep buying her courses in the future.
vishnuramanR
Udemy student
I particularly appreciate how you make the topics meaningful by explaining them in a practical and relatable manner. Your examples help connect theoretical knowledge with real-world understanding. This makes the concepts easier to remember and apply. Thank you for providing such useful insights and making the course more valuable. Your teaching adds great depth to the overall learning experience!
Jerry K.
Udemy student
The way it was presented and explained was completely understandable and applicable to me. I often need additional examples for explanations to get a full understanding but I did not need to seek additional information while listening to these videos
Lionnel M.
Udemy student
Very good
Sukanta B.
Udemy student
This perfectly matches with my objectives. I want to use what I learn in my research.
Fernando L.
Udemy student
Amazing course!
Fidelis C.
Udemy student
Its absolutely brilliant
Pierpaolo D.
Udemy student
Thanks Hania for the great course!!
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.
Varga-Henn M.
Udemy student
Well detailed introduction!
Francisco O.
Udemy student
Once again another fantastic course, it begins slowly but it ends with a nice but challenging introduction to combinatorics
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.
Stephen P.
Udemy student
Our professor is extremely clear and realistic about the objectives of this course and I am beyond excited. Her response time to messages is unrivaled.
Toby W.
Udemy student
Some of the best explanations I have ever seen and heard. The level of understanding she presented is a plus.
Łukasz D.
Udemy student
NIc dodać nic ująć.Machine translation: Nothing more, nothing less.
Levi B.
Udemy student
She seems like a great instructor with a great structure to the course
Axel S.
Udemy student
All courses from Hania are excellent and this is true for this one as well!
Mohammed G.
Udemy student
You are unique mathematician I studied in 4 continents and never seen such simple way with complex topics .. we owe you a lot Hania
SHIBAJI M.
Udemy student
The lectures made difficult topics easy to understand
Nicolás R.
Udemy student
It's amazing. I was looking for a course that could help me improve for my discrete mathematics class at the university and this has everything that I needed. I'm really thankful for this course.
Angelo C.
Udemy student
Corso super consigliato se volete migliorare la logica. Non sono laureato, ma lavoro come sviluppatore software e insegnante di informatica, e vi posso garantire che mi è servito tantissimo.Machine translation: I highly recommend this course if you want to improve your logical thinking. I don't have a college degree, but I work as a software developer and computer science teacher, and I can assure you that it has been incredibly helpful to me.
Sachin K.
Udemy student
Professor Hania's teaching is Math ASMR.
Jeffrey B.
Udemy student
Great Teacher....Slow...Methodical....Excellent Explanations !!
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.
Nomboh Q.
Udemy student
really interesting and i love the way she teaches
Peter S.
Udemy student
Only just started this course so cannot review. I have other Hania courses so I am expecting great things.
John H.
Udemy student
Hania, has or will soon have 13 courses on Udemy. They are excellent prep for Engineering or any STEM degree. I would recommend any high school student planning on a STEM degree, review as many of her courses as possible, before first year. She breaks the subject matter down and thoroughly explains it.
Bill M.
Udemy student
Instructor is very thorough in explaining what is required to understand this first part of Discrete Maths. Tons of lecture slides and notes and even recommendations for further study. Exceptional and highly recommended!!
Matteo M.
Udemy student
I can't have higher expectations not met by this course.
I have already followed other Prof. Hania's courses, which are always of top quality, with a focus on detailed and clear explanations.
Personally, I find these courses very useful for getting back to the basics and gaining new insights that I may have overlooked in my past instruction.
I have already followed other Prof. Hania's courses, which are always of top quality, with a focus on detailed and clear explanations.
Personally, I find these courses very useful for getting back to the basics and gaining new insights that I may have overlooked in my past instruction.
Karan K.
Udemy student
Builds the concept in a systematic manner
Leviathan G.
Udemy student
Very detailed and organized. I’m excited to begin learning.
Dr. S.
Udemy student
Great course
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.
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.
C T.
Udemy student
Very clear explanations and good examples.
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.