Essential tools for Understanding Statistics & Probability - Rules, Concepts, Variables, Equations

- Descriptive Statistics

- Probability

- Sampling Distributions

- Statistical Inference

This book is an English translation of the last French edition of Bourbaki's Functions of a Real Variable. The first chapter is devoted to derivatives, Taylor expansions, the finite increment's theorem, convex functions. In the second chapter, primitives and integrals (on arbitrary intervals) are studied, as well as their dependence with respect to parameters. Classical functions (exponential, logarithmic, circular and inverse circular) are investigated in the third chapter. The fourth chapter gives a thorough treatment of differential equations (existence and unicity properties of solutions, approximate solutions, dependence on parameters) and of systems of linear differential equations. The local study of functions (comparison relations, asymptotic expansions) is treated in chapter V, with an appendix on Hardy fields. The theory of generalized Taylor expansions and the Euler-MacLaurin formula are presented in the sixth chapter, and applied in the last one to the study of the Gamma function on the real line as well as on the complex plane. Although the topics of the book are mainly of an advanced undergraduate level, they are presented in the generality needed for more advanced purposes: functions allowed to take values in topological vector spaces, asymptotic expansions are treated on a filtered set equipped with a comparison scale, theorems on the dependance on parameters of differential equations are directly applicable to the study of flows of vector fields on differential manifolds, etc.

“One of the best critiques of current mathematics education I have ever seen.”—Keith Devlin, math columnist on NPR’s Morning Edition

A brilliant research mathematician who has devoted his career to teaching kids reveals math to be creative and beautiful and rejects standard anxiety-producing teaching methods. Witty and accessible, Paul Lockhart’s controversial approach will provoke spirited debate among educators and parents alike and it will alter the way we think about math forever.

Paul Lockhart, has taught mathematics at Brown University and UC Santa Cruz. Since 2000, he has dedicated himself to K-12 level students at St. Ann’s School in Brooklyn, New York. 

Engineering Mathematics, 5 Edition

John Bird "Engineering Mathematics, 5 Edition" 
Newnes | 2007 | ISBN: 0750685557 | 584 pages | PDF | 3,8 MB

John Bird's approach to mathematics, based on numerous worked examples supported by problems, is ideal for students of a wide range of abilities. Theory is kept to a minimum, with the emphasis firmly placed on problem-solving skills, making this a thoroughly practical introduction to the mathematics engineering students need to master.
The book presents a logical topic progression, rather than following the structure of a particular syllabus and is suitable for all Level 3 vocational students and first year undergraduates in Engineering. However, coverage has been carefully matched to the mathematics units within the 2007 BTEC National specifications.
In this fifth edition, new material on inequalities and differentiation of parametric equations, implicit and logarithmic functions as well as an introduction to differential equations has been added. The book now also includes two new revision tests and even more problems for students to work through.

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Finite Automata and Application to Cryptography mainly deals with the invertibility theory of finite automata and its application to cryptography. In addition, autonomous finite automata and Latin arrays, which are relative to the canonical form for one-key cryptosystems based on finite automata, are also discussed.

Finite automata are regarded as a natural model for ciphers. The Ra Rb transformation method is introduced to deal with the structure problem of such automata; then public key cryptosystems based on finite automata and a canonical form for one-key ciphers implementable by finite automata with bounded-error-propagation and without data expansion are proposed.

The book may be used as a reference for computer science and mathematics majors, including seniors and graduate students.

Renji Tao is a Professor at the Institute of Software, Chinese Academy of Sciences, Beijing.

Mathematical modeling using dynamical systems and partial differential equations is now playing an increasing role in the understanding of complex multi-scale phenomena. Behavior in seemingly different areas such as sociology, economics, and the life sciences can be described by closely related models. Systems made out of a large enough number of individual members can be said to exhibit a collective behavior, from which insight can be gathered in a way that real life experiments cannot.

Using examples from financial markets and modern warfare to the flocking of birds and the swarming of bacteria, the collected research in this volume demonstrates the common methodological approaches and tools for modeling and simulating collective behavior.

Specific topics covered include: analysis of wealth distributions, dynamics of price formation, spreading of opinions, models of social behavior, population dynamics, and aggregation and swarming.

This introduction presents the mathematical theory of probability for readers in the fields of engineering and the sciences who possess knowledge of elementary calculus. Presents new examples and exercises throughout. Offers a new section that presents an elegant way of computing the moments of random variables defined as the number of events that occur. Gives applications to binomial, hypergeometric, and negative hypergeometric random variables, as well as random variables resulting from coupon collecting and match models. Provides additional results on inclusion-exclusion identity, Poisson paradigm, multinomial distribution, and bivariate normal distribution A useful reference for engineering and science professionals.

This book is intended as a popular, but abbreviated treatise on probability theory. Basic concepts and techniques are introduced and illustrated mainly by drawing from a wealth of entertaining, paradoxical, and mind-boggling probability problems (such as the birthday problem or the Monty Hall problem). The writing style is purposefully enjoyable and mostly non-technical. The pace is leisurely. No knowledge of calculus of previous knowledge of probability theory or statistics is required. The emphasis is on entertainment and pedagogy rather than applicability or usefulness. Examples reflect everyday occurrences, not pre-fabricated or altered data. While honest in approach, the author takes great pain to ease the level of mathematics throughout the work. Probability theory is learned by and through example.

An 'analyst' is a mathematician who is seen habitually in the company of the real or complex numbers; a 'functional analyst' is an analyst who is not squeamish about using Zorn's lemma, definitely relishes the use of topology, and does not stand in the way of the internal algebraic impulses of the subject. The term 'functional analysis' dates from the early years of the subject, when abstract methods were novel and the principal motivation came from spaces whose elements are functions. Like other generic terms it is a catchall, encompassing a large part of the mathematical analysis of the last four decades. No portable textbook can hope to survey the subject. The present book is offered as a sampler. It is limited by my narrow glimpse of a vast domain, and biased in favor of operator theory.

• Publisher   Cambridge University Press
• Number Of Pages:   332
• Publication Date:   2005-01-20
• ISBN-10 / ASIN:   0521617200
• ISBN-13 / EAN:   9780521617208

Product Description:
Fractal structures are found everywhere in nature, and as a consequence anomalous diffusion has far reaching implications in a host of phenomena.

• Publisher:   Springer
• Number Of Pages:   540
• Publication Date:   2009-12-01
• ISBN-10 / ASIN:   1441900330
• ISBN-13 / EAN:   9781441900333

Product Description:
This book presents a systematic, comprehensive treatment of analog, discrete signal analysis and synthesis and an introduction to analog communication theory. The material is divided into five parts. The first part (Chapters 1-3) is mathematically oriented and deals with continuous-time (analog) signals. The second part (Chapters 4-5) is again mathematically based and deals with Fourier transforms, Hartley transforms, Laplace and Hilbert transforms. The third part (Chapters 6-7) presents basic analysis, approximations, and analog filter circuits using op-amps. The fourth part (Chapters 8-9) deals with discrete signals, fast algorithms and digital filters. The fifth part deals with an introduction to analog communication systems.

    *   Offers a conventional approach whereby continuous time signal is used to introduce discrete time signal in later chapters
    * Includes basics of MATLAB and MATLAB examples throughout the book
    * Provides over 400 detailed examples with  and over 400 homework problems
    * Provides an instructor solutions manual with completely worked solutions to all in text problems

This is a comprehensive and cohesive presentation of analog and digital signal processing and filtering for electrical engineers.   The author covers the principle concepts of analog and digital signals, generalized Fourier series approximations with sinusoidal and non-sinusoidal functions, and analog convolutions and correlations.   Signals and linear system interactions, system stability and bandwidths are also discussed. Analysis and design of analog low-pass, high-pass, band-pass, band elimination filters, and delay line filters are discussed using operational  Problems associated with nonlinear systems are included.