Algorithms in modern mathematics and computer science

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This text presents an in-depth overview of the algorithms and data structures that are central to modern mathematics and computer science. This text is designed for students and professionals who wish to understand and apply algorithmic concepts using modern methods. Main topics covered: Introduction to Algorithms: Definition of algorithms and their importance in mathematics and computer science. Presentation of algorithm evaluation criteria such as time and space complexity. Data Structures: Exploration of fundamental data structure types (arrays, lists, trees, graphs). Discussion of their importance in designing efficient algorithms. Sorting and Searching: Study of classic sorting algorithms (bubble sort, quick sort, merge sort) and search techniques (binary search). Comparison of the performance of these algorithms. Graph Algorithms: Analysis of graph traversal algorithms (DFS, BFS). Introduction to shortest path algorithms (Dijkstra, Bellman-Ford). Algorithm Analysis and Optimization: Algorithm analysis techniques to evaluate their effectiveness. Optimization methods to improve algorithm performance. Practical Applications: Concrete examples of algorithm applications in various fields, such as business intelligence and data analysis.