Algebra, Topology, Differential Calculus, And Optimization Theory For Computer Science And Engine

In the First four chapters, the basic algebraic structures (groups, rings, fields, vector spaces) are reviewed, with a major emphasis on vector spaces. Basic notions of linear alge- bra such as vector spaces, subspaces, linear combinations, linear independence, bases, quo- tient spaces, linear maps, matrices, change of bases, direct sums, linear forms, dual spaces, hyperplanes, transpose of a linear maps, are reviewed.

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

This modem introduction to the foundations of logic, mathematics, and computer science answers frequent questions that mysteriously remain mostly unanswered in other texts: • Why is the truth table for the logical implication so unintuitive? • Why are there no recipes to design proofs? • Where do these numerous mathematical rules come from?

This book gives a compact exposition of the fundamentals of the theory of locally convex topological vector spaces. Furthermore it contains a survey of the most important results of a more subtle nature, which cannot be regarded as basic, but knowledge which is useful for understanding applications. Finally, the book explores some of such applications connected with differential calculus and measure theory in infinite-dimensional spaces.