Description
Discrete Mathematics 3 is a problem-solving concepts and techniques course published by Udemy Online Academy. This course is an advanced mathematics program that focuses on the concepts and problem-solving techniques that form the foundation of computer science, mathematics, algorithms, and theoretical computing. Building on previous topics in discrete mathematics, this course examines advanced structures and methods used to analyze computational and logical problems. Students will study topics such as combinatorics, graph theory, recursion relations, discrete probability, mathematical reasoning, algorithms, and advanced proof techniques.
Through theoretical explanations and problem-solving exercises, participants will strengthen their ability to reason formally, analyze complex structures, and apply discrete mathematical concepts to real-world computer science and computational problems. Upon completion of this course, you will have a solid understanding of the problem-solving concepts and techniques that form the foundation of computer science, mathematics, algorithms, and theoretical computing.
What you will learn in Discrete Mathematics 3:
- A general introduction to sequences, with illustrations, guessing their closed formulas based on various descriptions and proving closed formulas by induction.
- Famous sequences (Fibonacci sequence, triangular numbers, tetrahedral numbers, perfect squares, powers of two) and their place in Pascal’s Triangle.
- Mathematical modelling and finding recursive formulas.
- Sequences of differences and sequences of partial sums.
- Arithmetic progressions and arithmetic sums.
- Geometric progressions and geometric sums.
- Monotone sequences with some examples (arithmetic and geometric progressions and their monotonicity).
- Periodic sequences with some examples (all of them based on elementary Number Theory and modulus).
- Polynomial sequences and their sequences of differences; a complete characterisation of such sequences and a method of finding their closed formula (Ansatz).
- Solving linear recursion with help of characteristic polynomials: the case of real zeros of various multiplicities; homogenous and non-homogenous.
- An introduction to generating functions for sequences.
- Some identities involving the Fibonacci numbers.
- An elementary introduction to some basic concepts in Graph Theory: isomorphic graphs, subgraphs, induced subgraphs, degree of a vertex, adjacency, cycles.
- Special graphs: trees, complete graphs K_n, paths P_n, cycles C_n, bipartite graphs, complete bipartite graphs K_(m,n), the Tutte Graph, the Petersen Graph.
- Trees and their basic properties.
- Planar graphs: Euler’s Formula.
- and …
Course specifications
Publisher: Udemy
Instructors: Hania Uscka-Wehlou and Martin Wehlou
Language: English
Level: Introductory to Advanced
Number of Lessons: 182
Duration: 53h 19m
Course topics
Discrete Mathematics 3 Prerequisites
Basic high school mathematics (mainly arithmetic)
Discrete Mathematics 1 (or equivalent: logic, sets, functions, relations, proof techniques, basic combinatorics)
Discrete Mathematics 2 (or equivalent: combinatorics, number theory, algebraic structures)
You are always welcome with your questions. If something in the lectures is unclear, please, ask. It is best to use QA, so that all the other students can see my additional explanations about the unclear topics. Remember: you are never alone with your doubts, and it is to everybody’s advantage if you ask your questions on the forum.
Pictures
Discrete Mathematics 3 introduction video
Installation guide
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Quality: 1080p
Downloadly link
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Size
58 GB