Course Summary
This course explores the fundamentals of discrete mathematics and their applications in computer science and beyond. Students will learn about topics such as logic, set theory, graph theory, and combinatorics.Key Learning Points
- Discrete mathematics is a fundamental subject for computer science and other fields.
- Students will learn how to think abstractly and solve complex problems.
- Knowledge of discrete mathematics can lead to career opportunities in fields such as software engineering, cryptography, and data analysis.
Job Positions & Salaries of people who have taken this course might have
- Software Engineer
- USA: $85,000 - $130,000
- India: ₹400,000 - ₹1,500,000
- Spain: €30,000 - €50,000
- Cryptographer
- USA: $90,000 - $150,000
- India: ₹500,000 - ₹2,000,000
- Spain: €35,000 - €60,000
- Data Analyst
- USA: $60,000 - $110,000
- India: ₹300,000 - ₹1,500,000
- Spain: €25,000 - €40,000
Related Topics for further study
Learning Outcomes
- Develop the ability to think abstractly and approach complex problems with a clear and logical mindset.
- Learn fundamental concepts in discrete mathematics and their applications in computer science and beyond.
- Gain valuable skills and knowledge that can lead to career opportunities in a variety of fields.
Prerequisites or good to have knowledge before taking this course
- Basic algebra skills
- Familiarity with mathematical notation
Course Difficulty Level
IntermediateCourse Format
- Online
- Self-paced
- Video lectures
- Assignments
- Quizzes
Similar Courses
- Introduction to Mathematical Thinking
- Mathematical Foundations for Cryptography
- Graph Algorithms
Related Education Paths
Notable People in This Field
- Richard Feynman
- Ronald Graham
Related Books
Description
Discrete mathematics forms the mathematical foundation of computer and information science. It is also a fascinating subject in itself.
Outline
- Introduction - Basic Objects in Discrete Mathematics
- Introduction to the course
- Sets, Relations, Functions
- Sets, relations, and functions
- Partial Orders
- Partial orderings: basic notions
- Mirsky's and Dilworth's Theorem
- Partial orders, maximal and minimal elements, chains, antichains
- Enumerative Combinatorics
- How to Count Functions, Injections, Permutations, and Subsets
- Evaluating Simple Sums
- Pascal's Triangle
- Counting Basic Objects
- The Binomial Coefficient
- Combinatorial Identities
- Estimating the Binomial Coefficient
- Excursion to Discrete Probability: Computing the Expected Minimum of k Random Elements from {1,...,n}
- An Eagle's View of Pascal's Triangle
- Asymptotics and the O-Notation
- Asymptotics and the O( )-Notation
- The Big-O-Notation
- Introduction to Graph Theory
- Basic Notions and Examples
- Graph Isomorphism, Degree, Graph Score
- Graph Score Theorem
- Graphs, isomorphisms, and the sliding tile puzzle
- Connectivity, Trees, Cycles
- Graphs and Connectivity
- Cycles and Trees
- An Efficient Algorithm for Isomorphism of Trees
- Cycles and Trees
- Eulerian and Hamiltonian Cycles
- Eulerian Cycles
- Hamilton Cycles - Ore's and Dirac's Theorem
- Hamiltonian Cycles and Paths
- Spanning Trees
- Minimum Spanning Trees
- The Number of Trees on n Vertices
- Spanning Trees
- Maximum flow and minimum cut
- Flow Networks, Flows, Cuts: Basic Notions and Examples
- Flow Networks: The Maxflow - Mincut Theorem
- Network flow
- Matchings in Bipartite Graphs
- Matchings in Bipartite Graphs - Basic Notions and an Algorithm
- Matchings in Bipartite Graphs: Hall's and König's Theorem
- Partial Orders: Dilworth's Theorem on Chains and Antichains
Summary of User Reviews
Coursera's Discrete Mathematics course has received positive reviews from users. Many users found the course useful for understanding the fundamentals of discrete mathematics.Key Aspect Users Liked About This Course
The course provides a comprehensive overview of discrete mathematics.Pros from User Reviews
- The course is well-structured and easy to follow.
- The material is presented in an engaging and interactive manner.
- The course content is relevant and useful for real-world applications.
- The instructor is knowledgeable and provides clear explanations.
- The course includes plenty of practice exercises and quizzes.
Cons from User Reviews
- Some users found the course challenging and difficult to understand.
- The course may require a significant time commitment to complete.
- The course may not be suitable for those with little prior math experience.
- Some users found the pacing of the course to be too fast.
- The course may not be as in-depth as some users were hoping for.
Dominik Scheder
3.4 Raiting
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