| Section | Conponents | ||
|---|---|---|---|
| Section 1 | Introduction to Numbers and Numbers Systems | ||
| Section 2 | Binary Numbers, Hexadecimal Numbers, Octal Numbers | ||
| Section 3 | Set Theory | ||
| Section 4 | Logic & Logic Networks | ||
| Section 5 | Functions 1: Mathematical Functions | ||
| Section 6 | Functions 2: Invertible Functions | ||
| Section 7 | Functions 3: O-Notation | ||
| Section 8 | Graph Theory | ||
| Section 9 | Trees, Binary Search Trees | ||
| Section 10 | Digraphs and Relation | ||
| Section 11 | Sequences and Series, with Telescoping Series | ||
| Section 12 | Proof by Induction, Convergence and Ratio Tests | ||
| Section 13 | Probability and Counting Problems | ||
| Section 14 | Matrices and Systems of Linear Equations |
Discrete mathematics is the common name for the fields of mathematics most generally useful in theoretical computer science. This includes computability theory, computational complexity theory, and information theory.
Computability theory examines the limitations of various theoretical models of the computer, including the most powerful known model
the Turing machine.
Complexity theory is the study of tractability by computer; some problems, although theoretically soluble by computer, are so expensive in terms of time or space that solving them is likely to remain practically unfeasible, even with rapid advance of computer hardware.
Finally, information theory is concerned with the amount of data that can be stored on a given medium, and hence concepts such as compression and entropy.
Sure! Here is the amended syllabus for a 16-week Discrete Mathematics course without a final exam:
Course Title: Discrete Mathematics for Computer Science
Course Description: This course provides an introduction to discrete mathematics with an emphasis on applications in computer science. Topics covered include logic, set theory, combinatorics, graph theory, functions, and discrete probability. These concepts form the foundational mathematical tools necessary for advanced topics in computer science, such as algorithms, data structures, and computer networks.
Prerequisites:
Basic knowledge of high school-level mathematics
Familiarity with fundamental programming concepts (recommended but not required)
Course Objectives:
Understand and apply fundamental concepts of discrete mathematics
Develop mathematical reasoning and problem-solving skills
Apply discrete mathematical techniques to computer science problems
Enhance the ability to communicate complex mathematical ideas effectively
Week 1: Introduction to Discrete Mathematics
Overview of discrete mathematics and its importance in computer science
Mathematical reasoning and proof techniques
Introduction to logic and propositions
Week 2: Logic and Proofs I
Propositional logic and logical connectives
Predicate logic and quantifiers
Week 3: Logic and Proofs II
Week 4: Sets and Relations I
Week 5: Sets and Relations II
Week 6: Functions I
Definitions and types of functions
Injective, surjective, bijective functions
Week 7: Functions II
Inverses of functions
Composition of functions and applications
Week 8: Combinatorics and Counting I
Basic counting principles: addition and multiplication rules
Permutations and combinations
Week 9: Combinatorics and Counting II
Binomial theorem and Pascal’s triangle
Inclusion-exclusion principle
Week 10: Advanced Counting Techniques
Pigeonhole principle
Recurrence relations and generating functions
Week 11: Graph Theory I
Introduction to graphs: terminology and types
Graph representations: adjacency matrix and list
Week 12: Graph Theory II
Graph traversal algorithms: BFS and DFS
Planar graphs and graph coloring
Week 13: Advanced Graph Theory
Eulerian and Hamiltonian paths and cycles
Network flows and graph connectivity
Week 14: Trees and Their Applications
Introduction to trees: terminology and properties
Binary trees and tree traversals
Spanning trees and minimum spanning trees
Week 15: Boolean Algebra and Computer Logic
Boolean functions and Boolean algebra
Simplification of Boolean expressions
Logic gates and digital circuits
Week 16: Discrete Probability
Basic concepts of probability theory
Conditional probability and Bayes’ theorem
Random variables and probability distributions
Assessment:
Weekly assignments and quizzes
Midterm exam
Project/Presentation (instead of a final exam)
Textbooks and Resources:
“Discrete Mathematics and Its Applications” by Kenneth H. Rosen
“Discrete Mathematics” by Richard Johnsonbaugh
Online resources and lecture notes
Instructor Contact:
Office hours: [Specify time]
Email: [Instructor’s email]
Course website: [Provide link]
This syllabus is now spread over 16 weeks and replaces the final exam with a project or presentation for comprehensive assessment. Let me know if you need any further adjustments or have any questions!