GMAT Focus | Quantitative| Master Math Course | 2026 Updated
Nadeem Arain
5.0 (853)·55h 15m · 544 lectures
$3.00$12–$199up to −98%
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Discrete Mathematics 3
Your third course in DM: sequences, recurrence relations, a brief introduction to Graph Theory, some applications of DM
5.011 reviews306 learners
- All Levels
- 53h 19m video
- 182 lectures
- English
- Captions
- Updated 2026
Taught by Hania Uscka-Wehlou
- 53h 19m of on-demand video
- 182 lectures across 12 sections
- One-off payment — no subscription
- Lifetime access on web and mobile
- Closed captions (English)
Curriculum
12 sections182 lectures53h 19m total
- Introduction to the course19:39
- Sequences in DM1 and DM216:19
- Graphs in DM16:40
- Applications of DM in DM1 and DM28:44
- How to study this section and which courses cover this stuff in depth5:52
- Solving systems of linear equations, two examples20:23
- Uniqueness of solutions of 2-by-2 systems of linear equations18:54
- Determinants of 2-by-2 and 3-by-3 matrices23:40
- Sarrus' rule for 3-by-3 matrices30:23
- Cramer's rule for solving 2-by-2 or 3-by-3 systems14:32
- What is a polynomial and how we know that two polynomials are equal7:06
- Exact polynomial fitting, a second-degree example20:26
- Exact polynomial fitting, a third-degree example14:33
- Solving quadratic equations using discriminants18:07
- Possible number of real zeros for a polynomial23:23
- Rational zeros of polynomials with integer coefficients28:53
- Polynomial division and why we need it46:50
- Partial fraction decomposition28:47
- Partial fraction decomposition, an example42:28
- Linear spaces and their subspaces, an (optional) topic for S714:40
- Linearly independent generators of a linear space, span (optional for S7)24:32
- Some words about rates of growth and derivatives43:06
- Sequences in Calculus versus sequences in DM22:30
- Sequences as functions; various ways of defining sequences24:30
- Determining formulas for sequences, an exercise28:09
- Recursion on example of factorial13:09
- Fibonacci sequence and modelling16:26
- Fibonacci sequence: closed formula26:24
- Fibonacci sequence: other examples of modelling15:50
- Modelling in combinatorics, some examples from our earlier courses12:13
- Two examples of sequences of two variables40:46
- Building a recursive formula based on a verbal description, the Tower of Hanoi11:53
- Back to the Tower of Hanoi: guess and prove the closed formula8:19
- Another one with some modelling13:55
- Triangular numbers and telescoping sums14:52
- A fun problem about triangular numbers and telescoping sums17:05
- Sequence of differences18:51
- Sequence of partial sums25:21
- Arithmetic operations on sequences13:28
- Vertical and horizontal shifts of sequences17:11
- (Optional) Vector space of all the sequences numbered with all natural numbers31:28
- Some examples of periodic sequences (much less relevant than the other stuff)11:54
- Some identities involving Fibonacci sequence, Problem 119:43
- Some identities involving Fibonacci sequence, Problem 220:27
- Some identities involving Fibonacci sequence, Problem 312:58
- Some identities involving Fibonacci sequence, Problem 417:46
- A real treat for your soul and eyes: plenty of celebrities in Pascal's Triangle16:00
- Arithmetic progressions, Exercise 117:55
- Arithmetic sums, Exercise 222:23
- Monotone sequences, Exercise 322:15
- Monotonicity of arithmetic progressions9:04
- Geometric progressions, Exercise 114:49
- Geometric sums, Exercise 224:34
- Monotonicity of geometric progressions10:56
- The rate of change of a geometric progression18:38
- A cute little problem involving integer numbers36:14
- Neither arithmetic nor geometric7:21
- Relevant videos from S2; polynomial sequences that we have already seen14:01
- First, second, third, etc, differences versus first, 2nd, 3rd, etc, derivatives18:46
- The one with making up sequences13:09
- A graphical illustration to the Reverse-and-Add method; reading recommendations15:40
- A counting problem with a polynomial sequence as a result8:04
- The theorem that characterises polynomial sequences24:58
- Necessary condition for polynomial sequences16:20
- Linearity of the operation of taking the differences of consecutive terms26:29
- Sufficient condition for polynomial sequences40:10
- Ansatz and undetermined coefficients24:00
- A bunch of problems with the same main determinant10:44
- The one with the toothpicks8:36
- The one with plenty of unit squares15:18
About this course
Discrete Mathematics 3 Mathematics from high school to university [None of our courses are produced using AI; they are all real-human products.] S1. Introduction to the course You will learn: about this course: its content and the optimal way of studying it together with the book. S2. Some preliminaries for the sections devoted to sequences You will learn: some basic algebraic techniques that are needed for the sections about sequences: solving systems of linear equations (2-by-2 and 3-by-3 determinant…
Before you start
- 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.
Who it’s for
- Students who plan to study mathematics at a college or university level, and want to gain some mathematical maturity to succeed
- High school students curious about university mathematics; the course is intended for purchase and supervision by adults for these students
- Everybody who wants to brush up their high school maths and gain a deeper understanding of the subject
- College and university students studying advanced courses, who want to understand all the details they might have missed in their earlier education
- Students who need mathematics for Computer Science, AI, ML, or other domains where one needs maths
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