
Explore fundamental rules of inference in logic, including modus ponens, disjunction and conjunction introduction, and truth tables, with practical examples and proofs.
Explore universal and existential quantifiers in logic, turning predicates into propositions across domains. Examine nested quantifiers, universal conditional propositions, and counter-examples in real and natural numbers.
Here is what we cover in this section:
Direct Proof
Indirect Proof
Induction
Other methods of proofs
As always you will have notes, problems, practice exercises, theory quizzes, ppt slides and progress quizzes in this section!
Thank you for your support!
Good luck!
Nikoloz Sanakoevi
Mikheil Chkeidze
Learn how direct proofs establish conclusions from hypotheses by constructing verifications, with examples on divisibility and even/odd integers, and explore core math terms like axioms, definitions, theorems, lemmas, and corollaries.
Learn how indirect proofs use contradiction and contrapositive by assuming the opposite and deriving a contradiction, with examples like even implies odd.
Explore induction as a three-step proof method—base case, induction hypothesis, and induction step—demonstrated with example proofs that verify equations via substitution and algebra.
Practice core proof techniques in discrete mathematics through exercises on even sums, equivalence of statements, contradiction, induction, and divisibility by seven.
Here is what we cover in this section:
Ordered Pair
Domain and Range
Functions and relations
Compositions and equivalence
More functions
All the materials included as always
Thank you for your support!
Good luck!
Nikoloz Sanakoevi
Mikheil Chkeidze
Explore exercises on functions and relations, solving domain and range, finding inverse relations, testing reflexivity, symmetry, and transitivity, and analyzing function composition and surjectivity.
Identify simple graphs with no loops or parallel edges and complete graphs K_n where every pair of vertices connects. Use the edge count n(n-1)/2.
Explore bipartite graphs, where vertices split into two disjoint sets with edges only between sets; learn to recognize complete bipartite graphs that connect every vertex across sets.
Identify circuits in graphs as closed paths that start and end at the same vertex, with simple circuits having no repeated vertices; note acyclic graphs contain no circuits.
Explore hamiltonian paths and hamiltonian circuits in graph theory, defining a path that visits every vertex once and a circuit that returns to the start, with example graphs and solutions.
Explore the division algorithm, expressing x as yq + r with 0 ≤ r < y, and divisibility theorems like x divides y and x divides y ± z.
Explore exercises on divisibility, proving that x divides a y plus b for integers a and b, and that x divides x y, with cube difference and three consecutive numbers.
Master permutations and combinations through hands-on exercises, including group selection, rearranging letters in mathematics, forming three-digit numbers from digits 1–3, and three-letter words from love.
This is a great place to learn Discrete Mathematics! Master Discrete Mathematics Today and Enroll Now!
In this course you will learn discrete mathematics and study mathematical logic, mathematical proofs, set theory, functions, relations, graph theory, number theory as well as combinations and permutations.
Each chapter of the course can be taken independently if required, and each chapter covers all of the listed topics in details so you will study everything that is necessary and in the order that most suits you as a student. As students usually come to this course for specific topic(s) and exercises, here is the comprehensive list of what you will learn from each chapter of this course:
Every lecture on these topics in discrete math is in high quality - 1080p and the powerpoint presentations are downloadable. (you can use them when you will need and they can save you time by revisiting the learned material as well). All the concepts and definitions are explained in the videos and each topic is ending with a set of examples as well as a small theory quiz (optional). We will go through each step to solve the given examples in each lesson as well as practice them at the end of each of the 7 chapters. In case of difficulties, you can post a question and get help from the instructors! You will have everything to learn discrete mathematics!
This course will be useful to anyone studying discrete math and any related subject to discrete mathematics, such as linear algebra, calculus, economics, statistics, cryptography, finance, actuarial science, data structures, data science or algorithms. And if you are a computer science student and you were searching for mathematics for computer science than you will definitely need to go through this training! This is also a great start for computer and math related majors, because they usually require a solid knowledge in discrete math.
The instructors have both completed discrete mathematics in there computer engineering sophomore year and got the A+ (4.0) grade in discrete math which has lead to the idea of creating this training. We have seen how our university students in fields such as computer science, computer engineering and electrical engineering were struggling to study the material and worried about passing their exams. And if you are tired of learning everything on your own with university or from professors while going to the lectures everyday, you can now get these lessons for as little as two cups of coffee and this small investment will rapidly effect your life, career and especially your GPA! So make the right decision today and enroll now! Learn discrete Mathematics Today!
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After enrolling you will feel 100% confident and will master your skills in Discrete Math. You will have all necessary materials to revisit and videos with lifetime access that you can watch even on your phone, laptop or TV screen. You will solve the problems in discrete math step-by-step and even know all the theory and concepts that are necessary for your success in this subject. Feel free to look at the free materials that are provided to you on this page. All the powerpoint presentations are downloadable so that you will be able to simply skim through them in 20 minutes if you will need to repeat some material or prepare for your class.
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