Algorithm Analysis is a course that explores the mathematical foundations of computer algorithms and their performance analysis. In this course, students will gain a deep understanding of the principles behind the design and analysis of algorithms, including basic data structures, algorithmic paradigms, and optimization techniques.

The course is designed to equip students with the necessary tools to analyze the time and space complexity of algorithms, and to evaluate their performance in terms of worst-case, average-case, and best-case scenarios. Through a combination of lectures, problem-solving sessions, and programming assignments, students will develop a solid grasp of algorithmic design and analysis.

Topics covered in the course include:

• Asymptotic analysis of algorithms, including big-O notation, omega notation, and theta notation
• Sorting algorithms, such as quicksort, mergesort, and heapsort
• Data structures, including arrays, linked lists, stacks, queues, and trees
• Dynamic programming and greedy algorithms
• Graph algorithms, such as Dijkstra's algorithm and Kruskal's algorithm
• NP-completeness and approximation algorithms

Upon completion of the course, students will be able to:

• Analyze the time and space complexity of algorithms using asymptotic notation
• Identify appropriate data structures and algorithmic paradigms for solving different types of problems
• Design and analyze algorithms using dynamic programming and greedy techniques
• Apply graph algorithms to solve problems in networking, transportation, and social networks
• Understand the limitations of computational complexity and the concept of NP-completeness
• Develop approximation algorithms for NP-complete problems

Overall, this course is a challenging but rewarding experience for students who are interested in the mathematical foundations of computer science and want to develop a strong understanding of algorithm design and analysis.