University of Toronto Mathematics Competition 2001 2015

Author: Edward J. Barbeau
Publisher: Springer
ISBN: 9783319281063
Release Date: 2016-04-13
Genre: Mathematics

This text records the problems given for the first 15 annual undergraduate mathematics competitions, held in March each year since 2001 at the University of Toronto. Problems cover areas of single-variable differential and integral calculus, linear algebra, advanced algebra, analytic geometry, combinatorics, basic group theory, and number theory. The problems of the competitions are given in chronological order as presented to the students. The solutions appear in subsequent chapters according to subject matter. Appendices recall some background material and list the names of students who did well. The University of Toronto Undergraduate Competition was founded to provide additional competition experience for undergraduates preparing for the Putnam competition, and is particularly useful for the freshman or sophomore undergraduate. Lecturers, instructors, and coaches for mathematics competitions will find this presentation useful. Many of the problems are of intermediate difficulty and relate to the first two years of the undergraduate curriculum. The problems presented may be particularly useful for regular class assignments. Moreover, this text contains problems that lie outside the regular syllabus and may interest students who are eager to learn beyond the classroom.

Mathematical Fallacies Flaws and Flimflam

Author: Edward Barbeau
Publisher: MAA
ISBN: 0883855291
Release Date: 2000-06-15
Genre: Mathematics

Through hard experience mathematicians have learned to subject even the most 'evident' assertions to rigorous scrutiny, as intuition and facile reasoning can often be misleading. However, errors can slip past the most watchful eye, they are often subtle and difficult to detect; but when found they can teach us a lot and can present a real challenge to straighten out. This book collects together a mass of such errors, drawn from the work of students, textbooks, and the media, as well as from professional mathematicians themselves. Each of these items is carefully analysed and the source of the error is exposed. All serious students of mathematics will find this book both enlightening and entertaining.

Contests in Higher Mathematics

Author: Gabor J Szekely
Publisher: Springer Science & Business Media
ISBN: 9781461207337
Release Date: 2012-12-06
Genre: Mathematics

One of the most effective ways to stimulate students to enjoy intellectual efforts is the scientific competition. In 1894 the Hungarian Mathematical and Physical Society introduced a mathematical competition for high school students. The success of high school competitions led the Mathematical Society to found a college level contest, named after Miklós Schweitzer. The problems of the Schweitzer Contests are proposed and selected by the most prominent Hungarian mathematicians. This book collects the problems posed in the contests between 1962 and 1991 which range from algebra, combinatorics, theory of functions, geometry, measure theory, number theory, operator theory, probability theory, topology, to set theory. The second part contains the solutions. The Schweitzer competition is one of the most unique in the world. The experience shows that this competition helps to identify research talents. This collection of problems and solutions in several fields in mathematics can serve as a guide for many undergraduates and young mathematicians. The large variety of research level problems might be of interest for more mature mathematicians and historians of mathematics as well.

Berkeley Problems in Mathematics

Author: Paulo Ney de Souza
Publisher: Springer Science & Business Media
ISBN: 0387204296
Release Date: 2004-01-08
Genre: Mathematics

This book collects approximately nine hundred problems that have appeared on the preliminary exams in Berkeley over the last twenty years. It is an invaluable source of problems and solutions. Readers who work through this book will develop problem solving skills in such areas as real analysis, multivariable calculus, differential equations, metric spaces, complex analysis, algebra, and linear algebra.

Polynomials

Author:
Publisher: Springer Science & Business Media
ISBN: 9783642040122
Release Date: 2009
Genre: Polynomials


Servants of Globalization

Author: Rhacel Parreñas
Publisher: Stanford University Press
ISBN: 9780804796187
Release Date: 2015-08-26
Genre: Social Science

Servants of Globalization offers a groundbreaking study of migrant Filipino domestic workers who leave their own families behind to do the caretaking work of the global economy. Since its initial publication, the book has informed countless students and scholars and set the research agenda on labor migration and transnational families. With this second edition, Rhacel Salazar Parreñas returns to Rome and Los Angeles to consider how the migrant communities have changed. Children have now joined their parents. Male domestic workers are present in significantly greater numbers. And, perhaps most troubling, the population has aged, presenting new challenges for the increasingly elderly domestic workers. New chapters discuss these three increasingly important constituencies. The entire book has been revised and updated, and a new introduction offers a global, comparative overview of the citizenship status of migrant domestic workers. Servants of Globalization remains the defining work on the international division of reproductive labor.

The IMO Compendium

Author: Dušan Djukić
Publisher: Springer Science & Business Media
ISBN: 9780387334301
Release Date: 2006-06-07
Genre: Mathematics

This is the ultimate collection of challenging high-school-level mathematics problems. It is the result of a two year long collaboration to rescue these problems from old and scattered manuscripts, and produce the definitive source of IMO practice problems in book form for the first time. This book attempts to gather all the problems and solutions appearing on the IMO and contains a grand total of 1900 problems. It is an invaluable resource for high-school students preparing for mathematics competitions, and for anyone who loves math.

Writing Proofs in Analysis

Author: Jonathan M. Kane
Publisher: Springer
ISBN: 9783319309675
Release Date: 2016-05-28
Genre: Mathematics

This is a textbook on proof writing in the area of analysis, balancing a survey of the core concepts of mathematical proof with a tight, rigorous examination of the specific tools needed for an understanding of analysis. Instead of the standard "transition" approach to teaching proofs, wherein students are taught fundamentals of logic, given some common proof strategies such as mathematical induction, and presented with a series of well-written proofs to mimic, this textbook teaches what a student needs to be thinking about when trying to construct a proof. Covering the fundamentals of analysis sufficient for a typical beginning Real Analysis course, it never loses sight of the fact that its primary focus is about proof writing skills. This book aims to give the student precise training in the writing of proofs by explaining exactly what elements make up a correct proof, how one goes about constructing an acceptable proof, and, by learning to recognize a correct proof, how to avoid writing incorrect proofs. To this end, all proofs presented in this text are preceded by detailed explanations describing the thought process one goes through when constructing the proof. Over 150 example proofs, templates, and axioms are presented alongside full-color diagrams to elucidate the topics at hand.

Optimization of Polynomials in Non Commuting Variables

Author: Sabine Burgdorf
Publisher: Springer
ISBN: 9783319333380
Release Date: 2016-06-07
Genre: Mathematics

This book presents recent results on positivity and optimization of polynomials in non-commuting variables. Researchers in non-commutative algebraic geometry, control theory, system engineering, optimization, quantum physics and information science will find the unified notation and mixture of algebraic geometry and mathematical programming useful. Theoretical results are matched with algorithmic considerations; several examples and information on how to use NCSOStools open source package to obtain the results provided. Results are presented on detecting the eigenvalue and trace positivity of polynomials in non-commuting variables using Newton chip method and Newton cyclic chip method, relaxations for constrained and unconstrained optimization problems, semidefinite programming formulations of the relaxations and finite convergence of the hierarchies of these relaxations, and the practical efficiency of algorithms.

The Spectrum of Hyperbolic Surfaces

Author: Nicolas Bergeron
Publisher: Springer
ISBN: 9783319276663
Release Date: 2016-02-19
Genre: Mathematics

This text is an introduction to the spectral theory of the Laplacian on compact or finite area hyperbolic surfaces. For some of these surfaces, called “arithmetic hyperbolic surfaces”, the eigenfunctions are of arithmetic nature, and one may use analytic tools as well as powerful methods in number theory to study them. After an introduction to the hyperbolic geometry of surfaces, with a special emphasis on those of arithmetic type, and then an introduction to spectral analytic methods on the Laplace operator on these surfaces, the author develops the analogy between geometry (closed geodesics) and arithmetic (prime numbers) in proving the Selberg trace formula. Along with important number theoretic applications, the author exhibits applications of these tools to the spectral statistics of the Laplacian and the quantum unique ergodicity property. The latter refers to the arithmetic quantum unique ergodicity theorem, recently proved by Elon Lindenstrauss. The fruit of several graduate level courses at Orsay and Jussieu, The Spectrum of Hyperbolic Surfaces allows the reader to review an array of classical results and then to be led towards very active areas in modern mathematics.

The Stair Step Approach in Mathematics

Author: Hayk Sedrakyan
Publisher: Springer
ISBN: 9783319706320
Release Date: 2018-01-23
Genre: Mathematics

This book is intended as a teacher’s manual and as an independent-study handbook for students and mathematical competitors. Based on a traditional teaching philosophy and a non-traditional writing approach (the stair-step method), this book consists of new problems with solutions created by the authors. The main idea of this approach is to start from relatively easy problems and “step-by-step” increase the level of difficulty toward effectively maximizing students' learning potential. In addition to providing solutions, a separate table of answers is also given at the end of the book. A broad view of mathematics is covered, well beyond the typical elementary level, by providing more in depth treatment of Geometry and Trigonometry, Number Theory, Algebra, Calculus, and Combinatorics.

The IMO Compendium

Author: Dušan Djukić
Publisher: Springer Science & Business Media
ISBN: 1441998543
Release Date: 2011-05-05
Genre: Mathematics

"The IMO Compendium" is the ultimate collection of challenging high-school-level mathematics problems and is an invaluable resource not only for high-school students preparing for mathematics competitions, but for anyone who loves and appreciates mathematics. The International Mathematical Olympiad (IMO), nearing its 50th anniversary, has become the most popular and prestigious competition for high-school students interested in mathematics. Only six students from each participating country are given the honor of participating in this competition every year. The IMO represents not only a great opportunity to tackle interesting and challenging mathematics problems, it also offers a way for high school students to measure up with students from the rest of the world. Until the first edition of this book appearing in 2006, it has been almost impossible to obtain a complete collection of the problems proposed at the IMO in book form. "The IMO Compendium" is the result of a collaboration between four former IMO participants from Yugoslavia, now Serbia and Montenegro, to rescue these problems from old and scattered manuscripts, and produce the ultimate source of IMO practice problems. This book attempts to gather all the problems and solutions appearing on the IMO through 2009. This second edition contains 143 new problems, picking up where the 1959-2004 edition has left off.

Applied E Learning and E Teaching in Higher Education

Author: Donnelly, Roisin
Publisher: IGI Global
ISBN: 9781599048178
Release Date: 2008-07-31
Genre: Business & Economics

"This book presents international practices in the development and use of applied e-Learning and e-Teaching in the classroom in order to enhance student experience, add value to teaching practices, and illuminate best practices in the area of e-Assessment. This book provides insight into e-Learning and e-Teaching practices while exploring the roles of academic staff in adoption and application"--Provided by publisher.

Problem Solving Through Problems

Author: Loren C. Larson
Publisher: Springer Science & Business Media
ISBN: 9781461254980
Release Date: 2012-12-06
Genre: Mathematics

This is a practical anthology of some of the best elementary problems in different branches of mathematics. Arranged by subject, the problems highlight the most common problem-solving techniques encountered in undergraduate mathematics. This book teaches the important principles and broad strategies for coping with the experience of solving problems. It has been found very helpful for students preparing for the Putnam exam.

Geometric Inequalities

Author: Hayk Sedrakyan
Publisher: Springer
ISBN: 9783319550800
Release Date: 2017-06-29
Genre: Mathematics

This unique collection of new and classical problems provides full coverage of geometric inequalities. Many of the 1,000 exercises are presented with detailed author-prepared-solutions, developing creativity and an arsenal of new approaches for solving mathematical problems. This book can serve teachers, high-school students, and mathematical competitors. It may also be used as supplemental reading, providing readers with new and classical methods for proving geometric inequalities.