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The following video provides an outline of all the topics you would expect to see in a typical high school or college-level Discrete Math class.
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Discrete Math Course Topics
Discrete Math Overview
If you need help in discrete math, you’re in the right place. This course covers everything you need to tackle those questions that keep you up at night.
The following sections provide links to the complete lessons on all course topics.
Logic
6 Videos 105 Examples
- Propositional Logic
- Logical Implication
- Logical Equivalence
- Predicate Logic
- Rules of Inference
- Categorical Syllogism
- Chapter Test
Proofs
6 Videos 61 Examples
- Direct Proof
- Indirect Proof
- Proof By Cases
- Logic Proofs
- Proof By Induction
- Chapter Test
Set Theory
4 Videos 61 Examples
- Sets
- Set Operations
- Set Identities
- Chapter Test
Number Theory
5 Videos 68 Examples
- A Divides B
- Modular Arithmetic
- Greatest Common Divisor
- Boolean Algebra
- Chapter Test
Functions
7 Videos 89 Examples
- Types Of Functions
- Injective
- Surjective
- Bijection
- Asymptotic Notation
- Big O
- Chapter Test
Combinatorics
9 Videos 115 Examples
- Fundamental Counting Principle
- Permutation
- Combinations
- Pigeonhole Principle
- Binomial Coefficient
- Recursive Formula
- Iteration Method Recurrence
- Recurrence Relation
- Chapter Test
Relations
6 Videos 79 Examples
- Binary Relation
- Discrete Math Relations
- Equivalence Relation
- Partial Order
- Lattices
- Chapter Test
Trees And Graphs
8 Videos 89 Examples
- Graph Theory
- Isomorphic Graph
- Euler Circuit & Hamiltonian Path
- Tree Graph
- Spanning Tree
- Planar Graphs
- Graph Coloring
- Chapter Test
Common Questions
What’s the best way to learn discrete mathematics?
Read your textbook, complete examples and practice exercises, and have a willingness to learn. This course is different for most students as it doesn’t build upon prior classes. Discrete math focuses on concepts, theorems, and proofs; therefore, it’s important to read the textbook, practice example problems, and stay ahead of your assignments.
Why do computer science majors need to learn discrete math?
To put it simply, it’s because computers work in binary (i.e., digital 0s and 1s), unlike the natural world, which revolves around continuous functions (i.e., analog), and discrete math helps us to bridge the gap.
For starters, sorting algorithms (a considerable part of computer science) utilize graph theory to design and solve their traveling salesman-type problems. And set theory deals with object classification. Just think about how many algorithms are running within self-driving cars trying to determine the moving landscape at 55 mph.
Likewise, cryptography is based on number theory, which is essential to keeping our passwords safe in the digital world.
Needless to say, CS majors need to speak “discrete” in today’s modern world.
Do you need calculus for discrete math?
No. So, go ahead and take that huge sigh of relief — I know you want to.
All that is needed for success is a willingness to think outside the box and practice new concepts. While most universities have a calculus prerequisite, it is unnecessary to have previously taken calculus to understand and be successful in discrete math. Granted, if you have some prior knowledge of calculus or even differential equations, you will find some of the strategies and concepts familiar, but they aren’t necessary to your overall success.
What math do I need to learn before discrete mathematics?
Students with a solid understanding of algebra, geometry, and precalculus will do very well in discrete math. The course is designed to build upon previously learned concepts like “if, then” statements, sets and Venn diagrams, functions and relations, and counting and probability to develop a greater understanding of data structures and algorithms.
Can you learn discrete math on your own?
Yes. The key to learning anything new is to have a desire to learn. But you also need to have the right resources. Consequently, you want to acquire a textbook and possibly watch available video lectures, as they will guide your study, provide examples, and clarify hard-to-understand theorems. Thankfully there is an abundance of information and resources available, both free and paid, for discrete math, so you’re in good hands. And the best part of self-study is that you can learn at your own pace.
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