Discrete Mathematics Course
About the Course
Discrete Mathematics is a foundational course in mathematics and computer science that studies structures that are fundamentally discrete rather than continuous. Unlike calculus or classical analysis, which deal with smooth and continuous change, discrete mathematics focuses on countable, distinct, and separated objects. It provides essential theoretical tools for modern areas such as computer science, information technology, cryptography, artificial intelligence, and data science.
The course typically begins with mathematical logic, including propositional and predicate logic. Students learn how to construct and evaluate logical statements, develop truth tables, and understand logical equivalences and inference rules.
Another central topic is set theory, including sets, subsets, operations on sets, and Cartesian products. This is followed by relations and functions, including equivalence relations and partial orders.
A significant part of the course is combinatorics and counting techniques such as permutations, combinations, pigeonhole principle, and binomial coefficients.
The course also includes recurrence relations and mathematical induction, which are used for analyzing recursive processes and proving correctness of algorithms.
Graph theory is another key component, covering graphs, paths, connectivity, trees, and basic graph algorithms used in networks and computer science applications.
Throughout the course, students develop logical thinking, proof skills, and problem-solving abilities. Discrete Mathematics forms a bridge between theoretical mathematics and practical computational applications.
The course typically begins with mathematical logic, including propositional and predicate logic. Students learn how to construct and evaluate logical statements, develop truth tables, and understand logical equivalences and inference rules.
Another central topic is set theory, including sets, subsets, operations on sets, and Cartesian products. This is followed by relations and functions, including equivalence relations and partial orders.
A significant part of the course is combinatorics and counting techniques such as permutations, combinations, pigeonhole principle, and binomial coefficients.
The course also includes recurrence relations and mathematical induction, which are used for analyzing recursive processes and proving correctness of algorithms.
Graph theory is another key component, covering graphs, paths, connectivity, trees, and basic graph algorithms used in networks and computer science applications.
Throughout the course, students develop logical thinking, proof skills, and problem-solving abilities. Discrete Mathematics forms a bridge between theoretical mathematics and practical computational applications.
Instructor
Altayeva Aizhan Bakatkaliyevna
Assistant Professor, PhD in Mathematics
Altayeva Aizhan Bakatkaliyevna is an Assistant Professor at the Department of Mathematical Cybernetics and Mechanics (MKM). She holds a PhD in Mathematics and is an active member of the Zhas Gylym (Young Scientists) community.
She currently teaches a range of advanced mathematical disciplines, including Discrete Mathematics, Mathematical Logic, Mathematical Modeling, Model Theory, and Algebraic Geometry.
Her academic work is closely connected with developing students’ analytical thinking, rigorous reasoning, and strong problem-solving skills.
In addition to teaching, she is engaged in research in cryptography and has a strong and growing interest in Artificial Intelligence (AI). She actively explores AI technologies and aims to integrate modern computational approaches with fundamental mathematical theory.
Her scientific interests lie at the intersection of pure mathematics, theoretical computer science, and intelligent systems, contributing both to academic research and innovative educational practices.
She currently teaches a range of advanced mathematical disciplines, including Discrete Mathematics, Mathematical Logic, Mathematical Modeling, Model Theory, and Algebraic Geometry.
Her academic work is closely connected with developing students’ analytical thinking, rigorous reasoning, and strong problem-solving skills.
In addition to teaching, she is engaged in research in cryptography and has a strong and growing interest in Artificial Intelligence (AI). She actively explores AI technologies and aims to integrate modern computational approaches with fundamental mathematical theory.
Her scientific interests lie at the intersection of pure mathematics, theoretical computer science, and intelligent systems, contributing both to academic research and innovative educational practices.