Mathematical foundations

Ebook Concrete mathematics: A foundation for computer science (Second edition) presents the following content: Chapter 1: recurrent problems, chapter 2: sums, chapter 3: integer functions, chapter 4: number theory, chapter 5: binomial coefficients, chapter 6: special numbers, chapter 7: generating functions, chapter 8: discrete probability, chapter 9: asymptotics.

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Cryptography is concerned with the conceptualization, definition, and construction of computing systems that address security concerns. The design of cryptographic systems must be based on firm foundations. This book presents a rigorous and systematic treatment of the foundational issues: defining cryptographic tasks and solving new cryptographic problems using existing tools. It focuses on the basic mathematical tools: computational difficulty (one-way functions), pseudorandomness, and zero-knowledge proofs.

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This fifth edition of ‘Higher Engineering Mathematics’ covers essential mathematical material suitable for students studying Degrees, Foundation Degrees, Higher National Certificate and Diploma courses in Engineering disciplines. In this edition the material has been re-ordered into the following twelve convenient categories: number and algebra, geometry and trigonometry, graphs, vector geometry, complex numbers, matrices and determinants, differential calculus, integral calculus, differential equations, statistics and probability, Laplace transforms and Fourier series.

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Lecture "Fundamentals of optimization: Mathematical foundation" provides students with content about: Optimization problems; Notations, convex sets, convex functions; Taylor approximation;... Please refer to the detailed content of the lecture!

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Teaching mathematics in general and instructing mathematics at junior schools in particular not only create favorable conditions for students to develop essential and core competencies but also help students enhance mathematical competencies as a foundation for a good study of the subject and promote essential skills for society, in which mathematical communication skill is an important one.

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Ebook "Power laws, scale-free networks and genome biology" deals with crucial aspects of the theoretical foundations of systems biology, namely power law distributions and scale-free networks which have emerged as the hallmarks of biological organization in the post-genomic era. The chapters in the book not only describe the interesting mathematical properties of biological networks but moves beyond phenomenology, toward models of evolution capable of explaining the emergence of these features.

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Ebook "Deterministic kinetics in chemistry and systems biology: The dynamics of complex reaction networks" gives a concise overview of the mathematical foundations of kinetics used in chemistry and systems biology. The analytical and numerical methods used to solve complex rate equations with the widely used deterministic approach will be described, with primary focus on practical aspects important in designing experimental studies and the evaluation of data.

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Part 2 book "Quantum mechanics demystified" includes content: The mathematical structure of quantum mechanics III, the foundations of quantum mechanics, the harmonic oscillator, angular momentum, spin 1/2 systems, quantum mechanics in three dimensions.

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Part 1 book "Geometric phases in physics" includes content: Introduction and overview, anticipations, foundations, some applications and tests, practional statistics.

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Part 1 book "Engineering mathematics" includes content: Review of algebraic techniques; engineering functions; the trigonometric functions; coordinate systems; discrete mathematics; sequences and series; vectors; matrix algebra; complex numbers; differentiation; techniques of differentiation; applications of differentiation; integration.

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Part 2 book "Engineering mathematics" includes content: Techniques of integration; applications of integration; further topics in integration, numerical integration; Taylor polynomials, Taylor series and Maclaurin series, ordinary differential equations; ordinary differential equations; the Laplace transform; difference equations and the Z transform; fourier series; the Fourier transform; functions of several variables; vector calculus; line integrals and multiple integrals; probability; statistics and probability distributions.

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Part 1 book "Discrete mathematics and its applications" includes content: The foundations - logic and proofs; basic structures - sets, functions, sequences, sums, and matrices; algorithms; number theory and cryptography, induction and recursion; counting; discrete probability.

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Ebook "Introduction to mathematical methods in bioinformatics" looks at the mathematical foundations of the models currently in use. All existing books on bioinformatics are software-orientated and they concentrate on computer implementations of mathematical models of biology. This book is unique in the sense that it looks at the mathematical foundations of the models, which are crucial for correct interpretation of the outputs of the models.

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Part 1 book "Computer graphics programming in OpenGL with Java" includes content: Getting started, the OpenGL graphics pipeline, mathematical foundations, managing 3D graphics data, texture mapping, 3D models, lighting, shadows, sky and backgrounds.

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Part 1 book "Discrete mathematics and its applications" includes content: The foundations - logic and proofs; basic structures - sets, functions, sequences, sums, and matrices; algorithms; number theory and cryptography; induction and recursion; counting; discrete probability; advanced counting techniques; relations.

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Ebook "Big data in omics and imaging: Association analysis" addresses the recent development of association analysis and machine learning for both population and family genomic data in sequencing era. It is unique in that it presents both hypothesis testing and a data mining approach to holistically dissecting the genetic structure of complex traits and to designing efficient strategies for precision medicine.

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Part 1 of ebook "Financial products: An introduction using Mathematics and Excel" provides readers with contents including: an introduction to Excel; Chapter 1 - A foundation; Chapter 2 - Forward contracts; Chapter 3 - The futures market; Chapter 4 - Bonds;...

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Part 1 of ebook "Benford’s law: Applications for forensic accounting, auditing, and fraud detection" provides readers with contents including: introduction and mathematical foundations; theorems, truisms, and a little trivia; more formulas and facts, and a little fibonacci; primary benford’s law tests; advanced benford’s law tests; associated benford’s law tests;...

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Continued part 1, part 2 of ebook "ACCA approved interactive text: Foundations in accountancy FMA/ACCA paper F2 management accounting" provides readers with contents including: budgeting; capital expenditure budgeting; methods of project appraisal; standard costing; sales variances and operating statements; performance measurement; practice question and answer bank; formula sheet and mathematical tables; applications of performance measurement;...

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The following will be discussed in "Ebook An introduction to genetic algorithms" includes contents: Chapter 1: genetic algorithms: an overview; chapter 2: genetic algorithms in problem solving; chapter 3: genetic algorithms in scientific models; chapter 4: theoretical foundations of genetic algorithms; chapter 6: conclusions and future directions; Appendix A: Selected general references; Appendix B: Other resources.

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