Professional Math
Undergraduate course, University of Giresun, Department of Computer Engineering, 2020
The course covers a variety of mathematical topics such as Calculus, Linear Algebra, Discrete Math, Number theory, Probability and Statistics, Optimization, Boolean Algebra and Automata theory. These topics are essential for understanding the fundamentals of computer science and for solving problems in computer science fields such as algorithms, complexity theory, cryptography, computer networks, and artificial intelligence. By the end of the course, students will have a solid understanding of the mathematical concepts and techniques used in computer science and will be well-prepared to pursue advanced studies or professional careers in the field.
Chapter 1: Review of Calculus: functions, limits, derivatives, integrals
In this chapter, we will review the fundamental concepts of calculus, including functions, limits, derivatives, and integrals, which form the backbone of many mathematical models used in various fields such as engineering, physics, economics, and finance.
Chapter 2: Linear Algebra: vectors, matrices, systems of linear equations, eigenvalues and eigenvectors
Linear algebra is a fundamental branch of mathematics that deals with vectors, matrices, and systems of linear equations. This chapter will cover the basic concepts and techniques of linear algebra, including how to perform operations on vectors and matrices, solve systems of linear equations, and find eigenvalues and eigenvectors.
Chapter 3: Discrete Math: logic, set theory, counting principles, graph theory, relations and functions
In this chapter, we will explore the fundamentals of discrete mathematics, including logic, set theory, counting principles, graph theory, relations, and functions. These topics form the basis of various fields in computer science, such as algorithm design, cryptography, and artificial intelligence.
Chapter 4: Number theory and Cryptography
In this chapter, we will explore the fascinating world of number theory and its practical applications in cryptography. We will dive into prime numbers, modular arithmetic, and their role in creating secure communication systems.
Chapter 5: Probability and Statistics
The chapter on “Probability and Statistics” introduces the fundamental concepts and techniques for analyzing and interpreting data, making informed decisions, and modeling uncertainty in various real-world applications.
Chapter 6: Optimization and Linear Programming
This chapter explores the applications of optimization in various fields such as economics, finance, engineering, and management. It also delves into the mathematical foundations of linear programming, including the simplex method, duality theory, and sensitivity analysis, and provides a comprehensive understanding of how to use optimization tools to make better decisions in real-world scenarios.
Chapter 7: Boolean Algebra and Switching theory
The chapter “Boolean Algebra and Switching theory” in our professional math course focuses on the fundamentals of digital logic and the mathematical principles of Boolean algebra, as well as the applications of switching theory in electronic circuits and computer science.
Chapter 8: Graph algorithms
Graph algorithms allow us to analyze and manipulate complex structures represented by networks of nodes and edges, and are used in a wide variety of applications ranging from social network analysis to logistics optimization. We will study different types of graph algorithms and their applications, including shortest path algorithms, spanning tree algorithms, and graph traversal algorithms.
- Graph algorithms [pdf]
Chapter 9: Numerical Methods
The chapter on “Numerical Methods” is focused on introducing the fundamental concepts and techniques used in solving mathematical problems that cannot be solved analytically. These methods involve approximating solutions to problems using algorithms and computational techniques, making it an important area of study in various fields such as engineering, physics, and computer science.
- Numerical Methods [pdf]
Chapter 10: Formal Languages and Automata
This chapter introduces the concept of formal languages, grammar, and automata theory, which are essential for understanding the limits and capabilities of computing systems. Students will learn about regular expressions, context-free grammars, pushdown automata, and Turing machines, and how these concepts are applied in programming and software development.