- Quantifiers
- Sets
- Relations and Functions
Discrete Structures, Data Structures, and Algorithms
Master the essential principles of mathematical concepts such as data structure, algorithms, and discrete structures ...Read more
Online
₹ 799
Quick Facts
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Medium of instructions
English
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Mode of learning
Self study
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Mode of Delivery
Video and Text Based
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Course overview
Matthew Fried - Professor created the Discrete Structures, Data Structures, and Algorithms certification course, which is available on Udemy and is designed for students who want to improve their knowledge and expertise in mathematical concepts such as algorithms, data structures, and discrete structures. The goal of the Discrete Structures, Data Structures, and Algorithms online course by Udemy are to help students comprehend all of the mathematics and structures required to perform computing effectively.
Discrete Structures, Data Structures, and Algorithms online classes are designed to provide students with a systematic and comprehensive understanding of the major components of discrete structures, data structures, and algorithm foundations. Students will receive 29 hours of digital downloadable learning materials, as well as 56 downloadable resources, covering topics such as logic, proof, graphs, relations, sequences, series, set theory, graph theory, number theory, euclidean theorem, matrix chain multiplication, hashing, sorting, binary trees, graph math, and more.
The highlights
- Certificate of completion
- Self-paced course
- 29 hours of pre-recorded video content
- 56 downloadable resources
Program offerings
- Online course
- Learning resources. 30-day money-back guarantee
- Unlimited access
- Accessible on mobile devices and tv
Course and certificate fees
Fees information
certificate availability
Yes
certificate providing authority
Udemy
Who it is for
What you will learn
After completing the Discrete Structures, Data Structures, and Algorithms online certification, students will develop a solid understanding of the fundamentals associated with mathematical concepts like data structures, discrete structure, and algorithms for computing activities as well as will learn about functions of logic, graphs, proofs, stacks. Students will learn about the Euclidean algorithm as well as the foundations of set theory, number theory, graph theory, and the master theorem. Students will learn about probability, sequence, series, matrix chain multiplication, functions, relations, and recursion relations. Students will learn how to use linked lists, binary trees, C++, Big-O, dynamic programming, sorting, and hashing, among other things.
The syllabus
Sets
Logic
- Introduction to Logic
- Practice Problems with Logic
- Conditional Statements
- Practice and Validity of Arguments
- Testing Validity
- Application to Digital Logic Circuits
- Review of Some Problems related to Section 1 and 2
Quantified Statements and Mathematical Symbols
- Quantifiers 1
- Quantifiers 2
Elementary Proofs
- Introduction to Proofs
- Even and Odd Numbers
- Rational Numbers
- Divisibility and Breaking into Cases
- Proof by Contradiction and Contraposition
- Indirect Proofs: Sqrt(2) and the Infinitude of Primes
- Euclidean Algorithm
Review of Sections 1-4
- Practice Problems 1
- Practice Problems 2
- Practice Problems 3
- Practice Test with Answers
Sequences and Series
- Sequences: Summation and Product Notation
- Practice for Sequences
Induction
- Induction 1
- Induction 2
- Induction 3
- Induction 4
- Strong Induction
Recurrence Relations
- Introduction to Recursion
- Recursion by Iteration
Set Theory
- Introduction to Set Theory
Review: Recurrence Relations and Set Theory
- Review 1 of Recurrence Relations and Set Theory
- Review 2 of Recurrence Relations
Functions
- Functions 1
- Functions 2
- Functions 3
- Review of Functions
Relations
- Relations 1
- Modular Exponentiation and Modular Inverse Review
- Review of Relations
Probability
- Introduction to Probability
- Intuition and Counting in Probability
- Multiplication Rule and Tree Design
- Permutations
- Addition and Difference Rules
- Inclusion/Exclusion Principle
- Pigeon Hole Principle
- Combinations
- R-Combinations with Repetition Allowed
- Pascal's Triangle and Binomial Theorem
- Combinatorial Proof
- Expectation
Math of Graphs
- Graph Theory and Big-O Intro Review
C++ Review
- Arrays and Pointers
- Pointers to Pointers and Matrices
- Explanation of Arrays (1d and 2d)
- Using 2d Arrays - Magic Squares (and growth rates)
- Arrays and Pointers Practice / Vectors
- Classes
- Copy Constructor and Assignment Operator Design and Logic
- Move Semantics
- Templates
- Practice: Combinations, Palindrome, C-String
Linked Lists
- Introduction to Linked Lists
- Linked List as an ADT
- Practice Questions for Linked Lists and some general C++
Big-O Notation
- General Introduction to Growth of Functions
- Introduction to Algorithm Concepts and Approaches
- Big-O Definition
- Big-Omega and Big-Theta Definitions
- Big-O Rules and Reasoning
- Simple Case Studies in Big-O: Pattern Matching and Matrix Multiplication
- Big-O Practice Problems
- Subset Sum Algorithm Comparison with Big-O
- Permutation Algorithm and Big-O Comparison
- Exponentiation Algorithm Big-O Investigation
Master Theorem
- Iteration and Recursion Tree Methods
- Introduction to Master Theorem
Stacks and Queues
- Introduction to Stacks and Postfix Notation
Sorting
- Introduction to Sorting Concepts
- Using Lambdas to Make Drivers to Test Sorts
- Insertion Sort in Depth
- Shellsort
- Heapsort
- Mergesort
Non-Comparison Sorting
- Proof of the Generalized Lower Bound for Comparison Sorts
- Bucket Sort and Radix Sort (<vector<vector<string>> fixed length version)
- CountingRadixSort
Hashing
- Hashing Basics
- Introductory Application: Rabin-Karp Algorithm
- Chaining and Open Addressing
Trees
- Binary Trees
Dynamic Programming
- Definition of Dynamic Programming
- Matrix Chain Multiplication - Definition of the Problem
- Matrix Chain Multiplication - Solution
- Rod Cutting Problem
Graphs
- Graphs as a Data Structure
- Depth First Traversal
- Breadth First Search
- Dijkstra's Shortest Path (1) - Concept
- Dijkstra's Shortest Path (2) - Concept
Assorted Problems
- Fast Exponentiation (1)
- Fast Exponentiation (2)
- Fast Modular Exponentiation
- Lexicographic Permutation
Practice and Review Questions for Data Structures
- Review of Templates, Move, and Linked Lists
- Review Questions for Big-O and more
- Review of Stacks, Queues, and Sorting
- Review of Sorting and Recursion
- Review of Hashing and Trees