Math Fundamentals for Algorithms

This course provides a comprehensive introduction to the essential mathematical concepts that form the foundation of algorithmic problem-solving. Through a combination of lectures and hands-on exercises, students will gain a deep understanding of summations, products, bounding summations, set theory, probability, combinatorics, and recursion.

The course begins with an overview of summations and products, learning how to calculate and manipulate these important mathematical tools. They will also explore the concept of bounding summations, which involves finding upper bounds for summations in order to gain insights into their behavior.

The course then moves on to combinatorics, which is the study of counting and arranging objects. Students will learn how to apply combinatorial techniques to solve problems related to permutations, combinations, and the rule of product.

Next, the course covers set theory and probability, including concepts such as sample spaces, events, and conditional probability. Students will learn how to apply these concepts, such as calculating the probability of the outcomes of discrete random variables.

Finally, the course concludes with an exploration of recursion, which is a key technique in algorithmic problem-solving. Students will learn how to write recursive functions to solve a variety of problems, and they will gain an understanding of the principles behind recursion.

By the end of this course, students will have a solid foundation in the mathematical concepts that are essential for success in algorithmic problem-solving. They will be equipped with the knowledge and skills needed to tackle complex problems and develop innovative solutions using mathematical techniques.