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https://github.com/jamesquinlan/discrete-math

COS 280 - Discrete Mathematics at University of Southern Maine
https://github.com/jamesquinlan/discrete-math

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COS 280 - Discrete Mathematics at University of Southern Maine

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# Discrete Mathematics II

COS 280 - Discrete Mathematics II at the [University of Southern Maine](https://usm.maine.edu/cos/) offered in the [Department of Computer Science](https://usm.maine.edu/department-computer-science/).



[List of Undergraduate Computer Science Courses at USM Department of Computer Science](usm_cos.md)



## Course description



Discrete mathematics is the mathematics of computing. This course lays the foundation for students to succeed in upper-level computer science courses, most of which require understanding concepts from discrete mathematics. This course is designed for students to learn how to think logically and mathematically and practice fundamental techniques for solving problems in computer science. Topics include sequences, mathematical induction, recursion, set theory, graphs, trees, analysis of algorithms, and regular expressions. COS 280 is required for the Computer Science major (see all [requirements for Computer Science](https://catalog.usm.maine.edu/preview_program.php?catoid=13&poid=2601)).



### Prerequisites



Grade of C or higher in:



* MAT 145 - Discrete Mathematics I

* COS 160 - Structured Problem-Solving Java



## Learning Outcomes



By the end of this course, students will be able to:



* Read, comprehend, and construct mathematical proof arguments.

* Solve sequential, recursive, set, and number theoretic problems.

* Discuss graphs, trees, and finite-state machines related to real-world computational problems.

* Illustrate mathematical techniques for specifying, verifying, and analyzing computer algorithms.

* Identify various natural and relevant uses of discrete math in computer science (and the real world).



## Textbook




Epp, S. S. (2020). *Discrete Mathematics with Applications* (5th ed.). 



**Publisher**: Cengage Learning. 



**ISBN**: 978-1-337-69419-3.



## Grading



Grades will be based on a group project, in-class exercises, assignments, and participation:



* 40%: Exercises and assignments

* 20%: Quizzes

* 10%: Attendance and Participation

* 20%: Midterm Exam

* 10%: Final Exam



## Topics



Notes from textbook.



* [Direct Proof](topics/directproof1.txt)

* [Set Definitions](topics/sets1.txt)

* [Set Properties](topics/sets2.txt)

* [Graphs: Walks and Circuits](topics/walks.txt)

* [Matrix representation of graph: adjacency matrix](topics/adjacency-mat.txt)

* [Trees](topics/trees.txt)

* [Binary Trees](topics/binary-trees.txt)

* [Minimial Spanning Trees and Shortest Path Algorithms](topics/mst.txt)

* [Big O](topics/bigo.txt)

* [Analysis of Algorithms](topics/algo.txt)

* [Regular Languages/Regular Expressions](topics/regex.txt)



## Additional Resources



**Discrete Mathematics and its Applications by Kenneth H. Rosen**: One of the most widely used textbooks for Discrete Mathematics (besides Epp). It covers various topics and provides clear explanations, examples, and exercises. The book is known for its accessible writing style and comprehensive coverage.



**Concrete Mathematics: A Foundation for Computer Science by Ronald L. Graham, Donald E. Knuth, and Oren Patashnik**: This book is a bit more advanced and suited for students with advanced mathematical background; it’s highly regarded for its deep exploration of mathematical concepts relevant to computer science. It’s an excellent choice for students interested in the mathematical foundations of algorithms and computer programming.



**Discrete Mathematics: An Open Introduction by Oscar Levin**: This textbook takes a more open and interactive approach. It’s free online and covers the core topics of Discrete Mathematics. It includes exercises, examples, and interactive components that engage students in learning.



**Mathematics for Computer Science by Eric Lehman, F. Thomson Leighton, and Albert R. Meyer**: While this textbook is not exclusively focused on Discrete Mathematics, it provides a strong foundation in mathematical concepts relevant to computer science. It covers discrete mathematics topics, making it a suitable resource for students interested in discrete math and computer science.