DIRECT KNOWLEDGE

Basic Set Theory

That Anyone Can Learn. This book is for beginners who want to explore the fascinating world of logical reasoning, mathematical proofs, and set theory. The text is easy to follow and provides many examples that help readers understand the concepts discussed. Topics include propositional logic first-order logic, set theory, functions, and relations. Additionally, we introduce connection theory and concept theory. With the novel approach taken here, with this book as a guide, readers will soon be able to see the beauty and power of mathematical reasoning. More Information

Learning Number Theory

With Python. In this book, we cover the basics of elementary number theory. Topics begin with natural numbers, divisibility in the integers, and unique prime factorization. After that, we cover linear, quadratic, and polynomial congruence equations. While studying these topics we’ll also learn how to use python. In the second part, we introduce automating proofs in elementary number theory using python. We’ll do this by first studying Grobner Bases in polynomial rings and then making a connection between these rings and theorems involving integer divisibility. More Information

Learning Linear Algebra

With Python. In this book, we cover the basics of linear algebra. Topics include systems of linear equations, finite-dimensional vector spaces, linear transformations, and inner-product spaces. Determinants, eigenvalues, and eigenvectors are also covered. While we explore these topics we’ll also learn how to use python when doing linear algebra. In the second part, we detail the structure of a linear operator by providing an algorithm for the Jordan canonical form of a linear transformation using python. More Information

Single Variable Calculus

With Python. In this book, we cover the basics of a first and second-semester course in the calculus of a single variable. Topics include limits and continuous functions, derivatives and their applications, and integrals and their applications. Techniques of integration and then infinite sequences and series are detailed. While we’re learning calculus we’ll also be learning the python programming language. We’ll study calculus numerically, symbolically, and graphically. This three-prong approach allows us to engage in calculus, learn it faster, and explore it deeper. More Information

Multivariable Calculus

With Python. In this book, we’ll explore multivariable calculus using python. Topics include multivariable functions and their limits, partial derivatives, and their applications, and multiple integration and applications. We detail vector-valued functions and vector fields. Towards the end, vector calculus by examining vector fields, line integrals, surface integrals, and some marvelous theorems involving these integrals. In the finale, the theory of electromagnetism is revealed. More Information