Mathematical Foundations

1. **Discrete Mathematics:**
– Introduction to Discrete Mathematics
– Sets, Relations, and Functions
– Graph Theory and Trees
– Combinatorics and Discrete Probability
– Boolean Algebra and Logic Gates

2. **Algorithms and Complexity:**
– Fundamentals of Algorithms
– Big O Notation and Complexity Analysis
– Sorting and Searching Algorithms
– Graph Algorithms
– NP-Completeness and Computational Complexity

3. **Number Theory and Cryptography:**
– Basic Concepts in Number Theory
– Prime Numbers and Factoring
– Modular Arithmetic and Cryptographic Algorithms
– Public Key Cryptography
– Hash Functions and Digital Signatures

4. **Linear Algebra and Matrices:**
– Matrix Operations and Transformations
– Systems of Linear Equations
– Eigenvalues and Eigenvectors
– Applications of Linear Algebra in Computer Science
– Advanced Topics: Singular Value Decomposition

5. **Calculus for Computer Science:**
– Limits, Continuity, and Differentiation
– Integration and its Applications
– Multivariable Calculus Concepts
– Differential Equations
– Discrete vs. Continuous Mathematics

6. **Probability and Statistics:**
– Probability Fundamentals
– Random Variables and Probability Distributions
– Statistical Inference and Hypothesis Testing
– Regression Analysis and Correlation
– Applications of Statistics in Computer Science

7. **Formal Languages and Automata Theory:**
– Introduction to Formal Languages
– Finite Automata and Regular Expressions
– Context-Free Grammars
– Turing Machines and Computability
– Complexity Classes and Language Hierarchies

8. **Information Theory and Coding:**
– Introduction to Information Theory
– Entropy and Information Content
– Coding Theorems and Data Compression
– Error Correction and Coding
– Applications in Data Transmission and Storage

9. **Mathematical Logic and Proof Techniques:**
– Propositional and Predicate Logic
– Proof Strategies and Techniques
– Recursive Definitions and Structural Induction
– Program Verification and Logic in Computer Science
– Gödel’s Incompleteness Theorems

10. **Optimization and Operations Research:**
– Linear Programming and Optimization
– Integer Programming and Combinatorial Optimization
– Decision Analysis and Game Theory
– Network Flow and Transportation Problems
– Heuristics and Approximation Algorithms

Each of these categories can be a mini-series within your larger series, providing a comprehensive foundation in the mathematical concepts crucial to computer science.