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Practical Discrete Mathematics: Discover math principles that fuel algorithms for computer science and machine learning with Python
A practical guide simplifying discrete math for curious minds and demonstrating its application in solving problems related to software development, computer algorithms, and data science
Key FeaturesApply the math of countable objects to practical problems in computer scienceExplore modern Python libraries such as scikit-learn, NumPy, and SciPy for performing mathematicsLearn complex statistical and mathematical concepts with the help of hands-on examples and expert guidanceBook DescriptionDiscrete mathematics deals with studying countable, distinct elements, and its principles are widely used in building algorithms for computer science and data science. The knowledge of discrete math concepts will help you understand the algorithms, binary, and general mathematics that sit at the core of data-driven tasks.
Practical Discrete Mathematics is a comprehensive introduction for those who are new to the mathematics of countable objects. This book will help you get up to speed with using discrete math principles to take your computer science skills to a more advanced level.
As you learn the language of discrete mathematics, you'll also cover methods crucial to studying and describing computer science and machine learning objects and algorithms. The chapters that follow will guide you through how memory and CPUs work. In addition to this, you'll understand how to analyze data for useful patterns, before finally exploring how to apply math concepts in network routing, web searching, and data science.
By the end of this book, you'll have a deeper understanding of discrete math and its applications in computer science, and be ready to work on real-world algorithm development and machine learning.
What you will learnUnderstand the terminology and methods in discrete math and their usage in algorithms and data problemsUse Boolean algebra in formal logic and elementary control structuresImplement combinatorics to measure computational complexity and manage memory allocationUse random variables, calculate descriptive statistics, and find average-case computational complexitySolve graph problems involved in routing, pathfinding, and graph searches, such as depth-first searchPerform ML tasks such as data visualization, regression, and dimensionality reductionWho this book is forThis book is for computer scientists looking to expand their knowledge of discrete math, the core topic of their field. University students looking to get hands-on with computer science, mathematics, statistics, engineering, or related disciplines will also find this book useful. Basic Python programming skills and knowledge of elementary real-number algebra are required to get started with this book.
Table of ContentsKey Concepts, Notation, Set Theory, Relations, and FunctionsFormal Logic and Constructing Mathematical ProofsComputing with Base-n NumbersCombinatorics Using SciPyElements of Discrete ProbabilityComputational Algorithms in Linear AlgebraComputational Requirements for AlgorithmsStorage and Feature Extraction of Graphs, Trees, and NetworksSearching Data Structures and Finding Shortest PathsRegression Analysis with NumPy and Scikit-LearnWeb Searches with PageRankPrincipal Component Analysis with Scikit-Learn
Key FeaturesApply the math of countable objects to practical problems in computer scienceExplore modern Python libraries such as scikit-learn, NumPy, and SciPy for performing mathematicsLearn complex statistical and mathematical concepts with the help of hands-on examples and expert guidanceBook DescriptionDiscrete mathematics deals with studying countable, distinct elements, and its principles are widely used in building algorithms for computer science and data science. The knowledge of discrete math concepts will help you understand the algorithms, binary, and general mathematics that sit at the core of data-driven tasks.
Practical Discrete Mathematics is a comprehensive introduction for those who are new to the mathematics of countable objects. This book will help you get up to speed with using discrete math principles to take your computer science skills to a more advanced level.
As you learn the language of discrete mathematics, you'll also cover methods crucial to studying and describing computer science and machine learning objects and algorithms. The chapters that follow will guide you through how memory and CPUs work. In addition to this, you'll understand how to analyze data for useful patterns, before finally exploring how to apply math concepts in network routing, web searching, and data science.
By the end of this book, you'll have a deeper understanding of discrete math and its applications in computer science, and be ready to work on real-world algorithm development and machine learning.
What you will learnUnderstand the terminology and methods in discrete math and their usage in algorithms and data problemsUse Boolean algebra in formal logic and elementary control structuresImplement combinatorics to measure computational complexity and manage memory allocationUse random variables, calculate descriptive statistics, and find average-case computational complexitySolve graph problems involved in routing, pathfinding, and graph searches, such as depth-first searchPerform ML tasks such as data visualization, regression, and dimensionality reductionWho this book is forThis book is for computer scientists looking to expand their knowledge of discrete math, the core topic of their field. University students looking to get hands-on with computer science, mathematics, statistics, engineering, or related disciplines will also find this book useful. Basic Python programming skills and knowledge of elementary real-number algebra are required to get started with this book.
Table of ContentsKey Concepts, Notation, Set Theory, Relations, and FunctionsFormal Logic and Constructing Mathematical ProofsComputing with Base-n NumbersCombinatorics Using SciPyElements of Discrete ProbabilityComputational Algorithms in Linear AlgebraComputational Requirements for AlgorithmsStorage and Feature Extraction of Graphs, Trees, and NetworksSearching Data Structures and Finding Shortest PathsRegression Analysis with NumPy and Scikit-LearnWeb Searches with PageRankPrincipal Component Analysis with Scikit-Learn
- GenresMathematicsTextbooks
330 pages, Kindle Edition
Published February 22, 2021
14 people are currently reading
51 people want to read
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Displaying 1 - 2 of 2 reviews
December 30, 2021
The way this text whets one's appetite for learning mathematics is incredible. Applications of said mathematics to specific domains in Computer Science and Machine Learning is eye opening! I enjoyed reading this book a lot. I sure hope it will serve as an intriguing introductory literature for one curious to delve into understanding some algorithms under the hood!
March 2, 2025
This book serves as a great learning resource for first-year computer science students, covering foundational mathematical tools alongside Python—a practical language for hands-on problem-solving and programming fundamentals.
Structured into three parts, the book transitions from theory to application. It begins with mathematical concepts solvable by hand, gradually introduces algorithmic problem-solving with programming tools, and concludes with real-world applications using NumPy, SciPy, and Matplotlib. The progression ensures an easy-to-follow flow from fundamental theory to practical implementation.
The organization of topics allows for easy backtracking of core ideas when analyzing algorithmic problems. If a problem has a closed-form solution, concepts like formal logic, truth tables, set theory, probability, and combinatorics come into play. For optimization problems, familiarity with common data structures, their corresponding algorithms, complexity analysis, and matrix operations is essential. In cases where a problem isn't programmatically solvable, machine learning can be leveraged by analyzing feature correlations or engineering new features before feeding them into a model.
Key takeaways:
- Mathematical functions and programming functions share an intuitive connection: both define mappings from input to output. Deterministic functions in programming mirror function definitions in math, while set operations frequently appear in database queries.
- Truth tables help break down complex logical propositions and validate arguments, supporting proof techniques like transitivity, De Morgan’s laws, and the contrapositive method.
- Gaussian elimination efficiently solves small linear systems by transforming a matrix to reduced row echelon form (RREF). However, solvers may return results even for inconsistent systems, making it crucial to check the determinant beforehand.
- Algorithmic problem-solving follows a structured approach:
Start with a brute-force baseline and analyze its complexity using Big-O notation to determine traceability. Choose appropriate data structures to optimize efficiency, often borrowing from established algorithms. For example, multiplying an adjacency matrix by itself n times reveals whether a minimum-edge path exists between two vertices. Improve runtime performance through vectorization, enabling batch operations for greater efficiency.
Overall, the book provides a well-structured introduction to computational thinking, equipping readers with both theoretical foundations and practical programming skills.
Structured into three parts, the book transitions from theory to application. It begins with mathematical concepts solvable by hand, gradually introduces algorithmic problem-solving with programming tools, and concludes with real-world applications using NumPy, SciPy, and Matplotlib. The progression ensures an easy-to-follow flow from fundamental theory to practical implementation.
The organization of topics allows for easy backtracking of core ideas when analyzing algorithmic problems. If a problem has a closed-form solution, concepts like formal logic, truth tables, set theory, probability, and combinatorics come into play. For optimization problems, familiarity with common data structures, their corresponding algorithms, complexity analysis, and matrix operations is essential. In cases where a problem isn't programmatically solvable, machine learning can be leveraged by analyzing feature correlations or engineering new features before feeding them into a model.
Key takeaways:
- Mathematical functions and programming functions share an intuitive connection: both define mappings from input to output. Deterministic functions in programming mirror function definitions in math, while set operations frequently appear in database queries.
- Truth tables help break down complex logical propositions and validate arguments, supporting proof techniques like transitivity, De Morgan’s laws, and the contrapositive method.
- Gaussian elimination efficiently solves small linear systems by transforming a matrix to reduced row echelon form (RREF). However, solvers may return results even for inconsistent systems, making it crucial to check the determinant beforehand.
- Algorithmic problem-solving follows a structured approach:
Start with a brute-force baseline and analyze its complexity using Big-O notation to determine traceability. Choose appropriate data structures to optimize efficiency, often borrowing from established algorithms. For example, multiplying an adjacency matrix by itself n times reveals whether a minimum-edge path exists between two vertices. Improve runtime performance through vectorization, enabling batch operations for greater efficiency.
Overall, the book provides a well-structured introduction to computational thinking, equipping readers with both theoretical foundations and practical programming skills.
Displaying 1 - 2 of 2 reviews