Discrete Structures, Data Structures, and Algorithms from Udemy

This course is a full course in understanding all the mathematics and structures required to successfully do computing. It is a course in discrete structures, data structures, and algorithms. That means that we go through logic and proofs alongside the structures such as trees and graphs. This is the basis for understanding algorithms, recursion and much more. This course aims to give a clear and cogent understanding of the major parts to discrete structures. Anyone interested in computers should be learning this material well.

Data structures requires the understanding of certain mathematical concepts that are built here. It is imperative to understand computing from first principles. As such, we build and analyze different data structures with our firm mathematical foundation.

This course also discusses an introduction to algorithms. It develops many ideas related to speed and efficiency in algorithms. It has many deep ideas and approaches to be an effective, algorithmic computerista.

What's inside

Learning objectives

Discrete structures, data structures, and algorithms. the mathematics required for computing and the structures behind it all.

Students will learn the fundamentals of logic, proof, graph theory, number theory, data structures, and much more - all with application!

Discrete structures, data structures, and algorithms. the mathematics required for computing and the structures behind it all.
Students will learn the fundamentals of logic, proof, graph theory, number theory, data structures, and much more - all with application!

Syllabus

Sets

Quantifiers

Relations and Functions

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

Good to know

Know what's good

, what to watch for

, and possible dealbreakers

Helps learners with a background in logic and proofs, development of discrete structures, and understanding of algorithms and data structures

Features a structured outline with topics ranging from logic and proofs to data structures and algorithms

Covers essential topics in discrete mathematics, including sets, relations, functions, and graph theory

Suitable for learners with prior experience in computer science and programming who wish to enhance their foundation in theoretical computer science

Designed for intermediate to advanced learners who seek a comprehensive understanding of algorithms and data structures

Taught by an experienced instructor with a strong reputation in computer science education

Activities

Be better prepared before your course. Deepen your understanding during and after it. Supplement your coursework and achieve mastery of the topics covered in Discrete Structures, Data Structures, and Algorithms with these activities:

Review Set Theory Basics

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Refreshing your understanding of set theory will strengthen your foundation for the course's mathematical concepts.

Browse courses on Set Theory

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Review the concepts of sets, subsets, and operations on sets.
Practice solving problems involving set theory.

Organize Course Notes and Materials

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Organizing your notes and course materials will enhance your ability to review and retain key concepts.

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Gather all course notes, assignments, and materials.
Sort and categorize the materials based on topic or lecture.
Create a system for easy retrieval and review.

Join a Study Group

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Participating in a study group will provide opportunities to discuss concepts, share perspectives, and reinforce your understanding.

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Find or create a study group with classmates.
Establish regular meeting times and a study schedule.
Collaborate to review course materials, solve problems, and prepare for assessments.

Five other activities

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Build a Graph Data Structure

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Implementing a Graph data structure in your preferred programming language will solidify your understanding of graph theory and its applications.

Browse courses on Graph Theory

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Choose a programming language and development environment.
Research different Graph data structures and their properties.
Implement the Graph data structure using the chosen programming language.
Test and debug your implementation using various test cases.

Solve Recurrence Relations Problems

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Practice solving recurrence relations problems will strengthen your understanding of recursion and its applications in solving mathematical problems.

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Review the concept of recurrence relations.
Practice solving simple recurrence relations problems.
Learn techniques for solving more complex recurrence relations.
Attempt solving challenging recurrence relations problems.

Explore Graph Algorithms Using NetworkX

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Working through tutorials on NetworkX will provide practical experience in applying graph algorithms to real-world problems.

Browse courses on Graph Algorithms

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Familiarize yourself with the NetworkX library.
Follow tutorials on implementing graph algorithms using NetworkX.
Experiment with different graph algorithms on various datasets.

Explore Data Structures Visualizations

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Visualizations can enhance your understanding of how data structures work and their performance characteristics.

Browse courses on Data Structures

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Find resources that provide interactive visualizations of data structures.
Explore visualizations for different types of data structures.
Experiment with different operations on the data structures using the visualizations.

Develop a Decision Tree Algorithm

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Creating a Decision Tree algorithm from scratch will enhance your understanding of supervised learning techniques and their practical implementation.

Browse courses on Decision Trees

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Study the theory behind Decision Trees and their algorithms.
Choose a programming language and development environment.
Implement the Decision Tree algorithm using the chosen programming language.
Evaluate the performance of your implementation using various datasets.
Optionally, create visualizations to illustrate the decision-making process.

Career center

Learners who complete Discrete Structures, Data Structures, and Algorithms will develop knowledge and skills that may be useful to these careers:

Computer Scientist

A Computer Scientist conducts research in the field of computer science, including the development of new programming languages, algorithms, and software systems. Discrete Structures, Data Structures, and Algorithms can be very useful for a Computer Scientist as it provides a comprehensive understanding of the logic and structures used in computer science.

See salaries and explore the career path for Computer Scientist

Data Scientist

A Data Scientist uses scientific methods, processes, algorithms, and systems to extract knowledge and insights from data in various forms, both structured and unstructured. Discrete Structures, Data Structures, and Algorithms can be very useful for a Data Scientist as it provides a strong foundation in the mathematical and logical principles used in data analysis.

See salaries and explore the career path for Data Scientist

Software Engineer

A Software Engineer applies the principles of computer science and software design to the creation of computer software and applications. Common responsibilities include developing, maintaining, and improving software, as well as designing and implementing new features or systems. Discrete Structures, Data Structures, and Algorithms can be very useful for a Software Engineer as it teaches the fundamentals of logic, proof, graph theory, and data structures.

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Computer Programmer

A Computer Programmer designs, develops, tests, and maintains software applications and systems. Discrete Structures, Data Structures, and Algorithms can be very useful for a Computer Programmer as it teaches the fundamentals of logic, proof, graph theory, and data structures, all of which are essential for software development.

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Operations Research Analyst

An Operations Research Analyst uses mathematical and analytical techniques to solve complex problems in business and industry. Discrete Structures, Data Structures, and Algorithms can be very useful for an Operations Research Analyst as it provides a strong foundation in the mathematical and logical principles used in operations research.

See salaries and explore the career path for Operations Research Analyst

Information Security Analyst

An Information Security Analyst designs and implements security measures to protect an organization's computer systems and networks from unauthorized access, use, disclosure, disruption, modification, or destruction. Discrete Structures, Data Structures, and Algorithms can be very useful for an Information Security Analyst as it provides a good foundation in the mathematical and logical principles commonly used to secure computer systems and networks.

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Data Analyst

A Data Analyst collects, processes, and analyzes data to identify trends and patterns, and to make recommendations for改进ments. Discrete Structures, Data Structures, and Algorithms can be useful for a Data Analyst as it provides a good foundation in the mathematical and logical principles frequently used in data analysis.

See salaries and explore the career path for Data Analyst

Database Administrator

A Database Administrator manages and maintains database systems, ensuring the efficient and reliable operation of the database. Discrete Structures, Data Structures, and Algorithms can be useful for a Database Administrator as it provides a comprehensive understanding of the logic and structures used in database systems.

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Actuary

An Actuary uses mathematical and statistical techniques to assess risk and uncertainty. Discrete Structures, Data Structures, and Algorithms can be useful for an Actuary as it provides a good foundation in the mathematical and logical principles frequently used in actuarial science.

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Risk Analyst

A Risk Analyst uses mathematical and analytical techniques to assess and manage risk. Discrete Structures, Data Structures, and Algorithms can be useful for a Risk Analyst as it provides a good foundation in the mathematical and logical principles frequently used in risk analysis.

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Financial Analyst

A Financial Analyst provides advice to businesses and individuals on financial matters. Discrete Structures, Data Structures, and Algorithms may be useful for a Financial Analyst as it provides a good foundation in the mathematical and logical principles frequently used in financial analysis.

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Investment Analyst

An Investment Analyst provides advice to businesses and individuals on investment opportunities. Discrete Structures, Data Structures, and Algorithms may be useful for an Investment Analyst as it provides a good foundation in the mathematical and logical principles frequently used in investment analysis.

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Web Developer

A Web Developer designs, develops, and maintains websites and web applications. Discrete Structures, Data Structures, and Algorithms can be useful for a Web Developer as it provides a good foundation in the mathematical and logical principles frequently used in web development.

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Computer Systems Analyst

A Computer Systems Analyst examines how computer systems are used and apply their understanding to address business problems. The work of a Computer Systems Analyst is to bridge the gap between business and IT, they identify opportunities to improve systems and processes, and then design and implement those improvements. Discrete Structures, Data Structures, and Algorithms may be useful for a Computer Systems Analyst as it provides a comprehensive understanding of the logic and structures used in computer systems.

See salaries and explore the career path for Computer Systems Analyst

Systems Administrator

A Systems Administrator installs, configures, and maintains computer systems, networks, and applications. Discrete Structures, Data Structures, and Algorithms may be useful for a Systems Administrator as it provides a comprehensive understanding of the logic and structures used in computer systems.

See salaries and explore the career path for Systems Administrator