Mathematics

Twenty-One Lectures on Complex Analysis: A First Course By Alexander Isaev

Quandles and Topological Pairs: Symmetry, Knots, and Cohomology By Takefumi Nosaka

Solvability, Regularity, and Optimal Control of Boundary Value Problems for PDEs: In Honour of Prof. Gianni Gilardi By Pierluigi Colli

Leavitt Path Algebras By Gene Abrams

Experimental Design: With Applications in Management, Engineering and the Sciences, Second Edition By Paul D. Berger

Twenty-One Lectures on Complex Analysis: A First Course By Alexander Isaev

English | PDF | 2017 | 193 Pages | ISBN : 3319681699 | 3.32 MB

At its core, this concise textbook presents standard material for a first course in complex analysis at the advanced undergraduate level. This distinctive text will prove most rewarding for students who have a genuine passion for mathematics as well as certain mathematical maturity.

Primarily aimed at undergraduates with working knowledge of real analysis and metric spaces, this book can also be used to instruct a graduate course. The text uses a conversational style with topics purposefully apportioned into 21 lectures, providing a suitable format for either independent study or lecture-based teaching. Instructors are invited to rearrange the order of topics according to their own vision. A clear and rigorous exposition is supported by engaging examples and exercises unique to each lecture; a large number of exercises contain useful calculation problems. Hints are given for a selection of the more difficult exercises. This text furnishes the reader with a means of learning complex analysis as well as a subtle introduction to careful mathematical reasoning. To guarantee a student’s progression, more advanced topics are spread out over several lectures.

This text is based on a one-semester (12 week) undergraduate course in complex analysis that the author has taught at the Australian National University for over twenty years. Most of the principal facts are deduced from Cauchy’s Independence of Homotopy Theorem allowing us to obtain a clean derivation of Cauchy’s Integral Theorem and Cauchy’s Integral Formula. Setting the tone for the entire book, the material begins with a proof of the Fundamental Theorem of Algebra to demonstrate the power of complex numbers and concludes with a proof of another major milestone, the Riemann Mapping Theorem, which is rarely part of a one-semester undergraduate course.

Quandles and Topological Pairs: Symmetry, Knots, and Cohomology By Takefumi Nosaka

English | PDF,EPUB | 2017 | 138 Pages | ISBN : 9811067929 | 6.4 MB

This book surveys quandle theory, starting from basic motivations and going on to introduce recent developments of quandles with topological applications and related topics. The book is written from topological aspects, but it illustrates how esteemed quandle theory is in mathematics, and it constitutes a crash course for studying quandles.

More precisely, this work emphasizes the fresh perspective that quandle theory can be useful for the study of low-dimensional topology (e.g., knot theory) and relative objects with symmetry. The direction of research is summarized as “We shall thoroughly (re)interpret the previous studies of relative symmetry in terms of the quandle”. The perspectives contained herein can be summarized by the following topics. The first is on relative objects G/H, where G and H are groups, e.g., polyhedrons, reflection, and symmetric spaces. Next, central extensions of groups are discussed, e.g., spin structures, K2 groups, and some geometric anomalies. The third topic is a method to study relative information on a 3-dimensional manifold with a boundary, e.g., knot theory, relative cup products, and relative group cohomology.For applications in topology, it is shown that from the perspective that some existing results in topology can be recovered from some quandles, a method is provided to diagrammatically compute some “relative homology”. (Such classes since have been considered to be uncomputable and speculative). Furthermore, the book provides a perspective that unifies some previous studies of quandles.The former part of the book explains motivations for studying quandles and discusses basic properties of quandles. The latter focuses on low-dimensional topology or knot theory. Finally, problems and possibilities for future developments of quandle theory are posed.

Solvability, Regularity, and Optimal Control of Boundary Value Problems for PDEs: In Honour of Prof. Gianni Gilardi By Pierluigi Colli

English | PDF,EPUB | 2017 | 572 Pages | ISBN : 3319644882 | 16.33 MB

This volume gathers contributions in the field of partial differential equations, with a focus on mathematical models in phase transitions, complex fluids and thermomechanics. These contributions are dedicated to Professor Gianni Gilardi on the occasion of his 70th birthday.

It particularly develops the following thematic areas: nonlinear dynamic and stationary equations; well-posedness of initial and boundary value problems for systems of PDEs; regularity properties for the solutions; optimal control problems and optimality conditions; feedback stabilization and stability results. Most of the articles are presented in a self-contained manner, and describe new achievements and/or the state of the art in their line of research, providing interested readers with an overview of recent advances and future research directions in PDEs.

Leavitt Path Algebras By Gene Abrams

English | PDF,EPUB | 2017 | 296 Pages | ISBN : 1447173430 | 9.11 MB

This book offers a comprehensive introduction by three of the leading experts in the field, collecting fundamental results and open problems in a single volume.

Since Leavitt path algebras were first defined in 2005, interest in these algebras has grown substantially, with ring theorists as well as researchers working in graph C*-algebras, group theory and symbolic dynamics attracted to the topic. Providing a historical perspective on the subject, the authors review existing arguments, establish new results, and outline the major themes and ring-theoretic concepts, such as the ideal structure, Z-grading and the close link between Leavitt path algebras and graph C*-algebras. The book also presents key lines of current research, including the Algebraic Kirchberg Phillips Question, various additional classification questions, and connections to noncommutative algebraic geometry.

Leavitt Path Algebras will appeal to graduate students and researchers working in the field and related areas, such as C*-algebras and symbolic dynamics. With its descriptive writing style, this book is highly accessible.

Experimental Design: With Applications in Management, Engineering and the Sciences, Second Edition By Paul D. Berger

English | PDF,EPUB | 2017 (2018 Edition) | 644 Pages | ISBN : 331964582X | 19.44 MB

This text introduces and provides instruction on the design and analysis of experiments for a broad audience. Formed by decades of teaching, consulting, and industrial experience in the Design of Experiments field, this new edition contains updated examples, exercises, and situations covering the science and engineering practice.

This text minimizes the amount of mathematical detail, while still doing full justice to the mathematical rigor of the presentation and the precision of statements, making the text accessible for those who have little experience with design of experiments and who need some practical advice on using such designs to solve day-to-day problems. Additionally, an intuitive understanding of the principles is always emphasized, with helpful hints throughout.