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Elements of Mathematics
This textbook offers a rigorous presentation of mathematics before the advent of calculus. Fundamental concepts in algebra, geometry, and number theory are developed from the foundations of set theory along an elementary, inquiry-driven path. Thought-provoking examples and challenging problems inspired by mathematical contests motivate the theory, while frequent historical asides reveal the story of how the ideas were originally developed. Beginning with a thorough treatment of the natural numbers via Peano’s axioms, the opening chapters focus on establishing the natural, integral, rational, and real number systems. Plane geometry is introduced via Birkhoff’s axioms of metric geometry, a...
Foundations of Applied Mathematics, Volume 2
In this second book of what will be a four-volume series, the authors present, in a mathematically rigorous way, the essential foundations of both the theory and practice of algorithms, approximation, and optimization—essential topics in modern applied and computational mathematics. This material is the introductory framework upon which algorithm analysis, optimization, probability, statistics, machine learning, and control theory are built. This text gives a unified treatment of several topics that do not usually appear together: the theory and analysis of algorithms for mathematicians and data science students; probability and its applications; the theory and applications of approximatio...
Mathematics, Ideas and the Physical Real
"Originally published in French as Les Mathematiques, les idees et le reel physique. Librairie Philosophique, J. VRIN, 2006"--T.p. verso.
Mathematics of Discrete Structures for Computer Science
Mathematics plays a key role in computer science, some researchers would consider computers as nothing but the physical embodiment of mathematical systems. And whether you are designing a digital circuit, a computer program or a new programming language, you need mathematics to be able to reason about the design -- its correctness, robustness and dependability. This book covers the foundational mathematics necessary for courses in computer science. The common approach to presenting mathematical concepts and operators is to define them in terms of properties they satisfy, and then based on these definitions develop ways of computing the result of applying the operators and prove them correct....
STP Caribbean Mathematics
STP Maths is one of the best selling maths courses across the Caribbean. The new edition has been revised in line with the new CXC syllabus, and now includes the use of investigations with opportunities for group work. It provides complete coverage of the CXC syllabus for the CSEC examination.
Prelude to Mathematics
This lively, stimulating account of non-Euclidean geometry by a noted mathematician covers matrices, determinants, group theory, and many other related topics, with an emphasis on the subject's novel, striking aspects. 1955 edition.
