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The field of mathematics that studies the interactions between number theory and algebraic geometry is known as arithmetic geometry. This book provides an introduction to number theory and arithmetic geometry, the goal being to use geometry as the motivation to prove the main theorems in the book.

How do biological objects communicate, make structures, make measurements and decisions, search for food, i.e., do all the things necessary for survival? Designed for an advanced undergraduate audience, this book uses mathematics to begin to tell that story.

Provides an introduction to the fundamentals of enumeration for advanced undergraduates and beginning graduate students in the mathematical sciences. The book offers a careful and comprehensive account of the standard tools of enumeration and their application to counting problems for the fundamental structures of discrete mathematics.

A newly translated and revised edition of the most popular introductory textbook on the subject in Hungary. The book covers the usual topics of introductory number theory: divisibility, primes, Diophantine equations, and so on. It also introduces several more advanced topics, including congruences of higher degree and algebraic number theory.

Introduces the world of advanced mathematics using algebraic structures as a unifying theme. Having no prerequisites beyond precalculus and an interest in abstract reasoning, the book is suitable for students who are looking for an entry into discrete mathematics, induction and recursion, groups and symmetry, and plane geometry.

Graph theory is a fascinating and inviting branch of mathematics. The goal of this textbook is to present the fundamentals of graph theory to a wide range of readers. The author has included the shortest, most elegant, most intuitive proofs for modern and classic results while frequently presenting them in new ways.

Provides a careful, thorough, and rigorous introduction to linear algebra. The book adopts a conceptual point of view, focusing on the notions of vector spaces and linear transformations, and it takes pains to provide proofs that bring out the essential ideas of the subject.

Provides a compact course in modern cryptography. The mathematical foundations in algebra, number theory and probability are presented with a focus on their cryptographic applications. The text provides rigorous definitions and follows the provable security approach. The most relevant cryptographic schemes are covered.

Explores linear algebra with the view that it is an important gateway connecting elementary mathematics to more advanced subjects, such as advanced calculus, systems of differential equations, differential geometry, and group representations.

This book is derived from lecture notes for a course on Fourier analysis for engineering and science students at the advanced undergraduate or beginning graduate level. Beyond teaching specific topics and techniques, the author's goal is to help engineering and science students cultivate more advanced mathematical know-how.

Presents a careful treatment of calculus and its theoretical underpinnings from the constructivist point of view. This leads to an important and unique feature of this book: all existence proofs are direct, so showing that the numbers or functions in question exist means exactly that they can be explicitly calculated.

Introduces game theory and its applications from an applied mathematician's perspective, systematically developing tools and concepts for game-theoretic modelling in the life and social sciences. The book presents a unified account of the central ideas of both classical and evolutionary game theory.

Provides a careful introduction to the real numbers with an emphasis on developing proof-writing skills. The book continues with a logical development of the notions of sequences, open and closed sets (including compactness and the Cantor set), continuity, differentiation, integration, and series of numbers and functions.

Offers a rigorous and coherent introduction to the five basic number systems of mathematics - natural numbers, integers, rational numbers, real numbers, and complex numbers. The great merit of the book lies in its extensive list of exercises following each chapter. These exercises are designed to assist the instructor and to enhance the learning experience of the students.

Uses a problem-solving approach to actively engage students in the learning process. The book bridges the study of plane geometry and the study of curves and surfaces of non-constant curvature in three-dimensional Euclidean space.

Optimization Theory is an active area of research with numerous applications; many of the books are designed for engineering classes, and thus have an emphasis on problems from such fields. Covering much of the same material, in this volume there is less emphasis on coding and detailed applications as the intended audience is more mathematical.

Simultaneously emphasises both the foundational and the computational aspects of modern statistics. Engaging and accessible, this book is useful to undergraduate students with a wide range of backgrounds and career goals. The topics have been selected to reflect the current practice in statistics, where computation is an indispensible tool.

Offers beginning undergraduate mathematics students a first exposure to introductory logic, proofs, sets, functions, number theory, relations, finite and infinite sets, and the foundations of analysis. The book provides students with a quick path to writing proofs and a practical collection of tools that they can use in later mathematics courses such as abstract algebra and analysis.

Mathematical analysis is often referred to as generalized calculus. But it is much more than that. This book has been written in the belief that emphasizing the inherent nature of a mathematical discipline helps students to understand it better. A large variety of exercises and the inclusion of informal interpretations of many results and examples are included.

Linear algebra and matrix theory are fundamental tools for almost every area of mathematics, both pure and applied. This book combines coverage of core topics with an introduction to some areas in which linear algebra plays a key role, for example, block designs, directed graphs, error correcting codes, and linear dynamical systems.

Provides an introduction to the world of modern algebra. Beginning with concrete examples from the study of integers and modular arithmetic, the text steadily familiarises the reader with greater levels of abstraction as it moves through the study of groups, rings, and fields. The book is equipped with over 750 exercises suitable for many levels of student ability.

Takes a novel approach to the standard introductory material on groups, rings, and fields. This title offers a semi-historical journey through the early decades of the subject as it emerged in the revolutionary work of Euler, Lagrange, Gauss, and Galois. It focuses on the central problem of studying the solutions of polynomial equations.

Explains the basic concepts of financial derivatives, including put and call options, as well as more complex derivatives such as barrier options and options on futures contracts. This book presents topics such as Zero Coupon Bonds, forward rates, the yield curve, and several bond price models.

Provides a mathematical treatment of the introduction to qualitative differential equations and discrete dynamical systems. The treatment includes theoretical proofs, methods of calculation, and applications. The two parts of the book can be covered independently in one semester each or combined together into a year long course.

This is a textbook for a course in Honors Analysis (for freshman/sophomore undergraduates) or Real Analysis (for junior/senior undergraduates) or Analysis-I (beginning graduates). It is intended for students who completed a course in AP Calculus, possibly followed by a routine course in multivariable calculus and a computational course in linear algebra.