Functions and Graphs

Functions and Graphs
Author: James Tanton
Publisher: American Mathematical Soc.
Total Pages: 238
Release: 2018
Genre: Education
ISBN: 147044349X

A playful, readable, and thorough guide to precalculus, this book is directed at readers who would like a holistic look at the high school curriculum material on functions and their graphs. The exploration is presented through problems selected from the history of the Mathematical Association of America's American Mathematics Competition.

Teaching School Mathematics: Pre-Algebra

Teaching School Mathematics: Pre-Algebra
Author: Hung-Hsi Wu:
Publisher: American Mathematical Soc.
Total Pages: 407
Release: 2016-06-29
Genre: Education
ISBN: 1470427206

This is a systematic exposition of a major part of the mathematics of grades 5 to 8 (excluding statistics), written specifically for Common Core era teachers. It differs from other books for teachers in that the mathematics is correct, in the sense that all the concepts are clearly and correctly defined, and a grade-appropriate explanation (that is, proof) is given for every assertion. For example, it gives a precise definition of percent and explains how to use the definition to do all the standard problems about percent in an entirely routine manner. It also gives a leisurely explanation for “negative times negative is positive”. Another key feature is an intuitive introduction to plane geometry via rotations, translations, reflections, and dilations that, instead of treating these transformations as merely fun activities, shows how they make sense of the usual geometric topics in middle school, including congruence, similarity, length, area, and volume. In short, the readers will find in this volume a clear explanation of whatever was once puzzling to them in the mathematics of grades 5 to 8.

Harmonic Maass Forms and Mock Modular Forms: Theory and Applications

Harmonic Maass Forms and Mock Modular Forms: Theory and Applications
Author: Kathrin Bringmann
Publisher: American Mathematical Soc.
Total Pages: 409
Release: 2017-12-15
Genre: Mathematics
ISBN: 1470419440

Modular forms and Jacobi forms play a central role in many areas of mathematics. Over the last 10–15 years, this theory has been extended to certain non-holomorphic functions, the so-called “harmonic Maass forms”. The first glimpses of this theory appeared in Ramanujan's enigmatic last letter to G. H. Hardy written from his deathbed. Ramanujan discovered functions he called “mock theta functions” which over eighty years later were recognized as pieces of harmonic Maass forms. This book contains the essential features of the theory of harmonic Maass forms and mock modular forms, together with a wide variety of applications to algebraic number theory, combinatorics, elliptic curves, mathematical physics, quantum modular forms, and representation theory.

Introduction to Representation Theory

Introduction to Representation Theory
Author: Pavel I. Etingof
Publisher: American Mathematical Soc.
Total Pages: 240
Release: 2011
Genre: Mathematics
ISBN: 0821853511

Very roughly speaking, representation theory studies symmetry in linear spaces. It is a beautiful mathematical subject which has many applications, ranging from number theory and combinatorics to geometry, probability theory, quantum mechanics, and quantum field theory. The goal of this book is to give a ``holistic'' introduction to representation theory, presenting it as a unified subject which studies representations of associative algebras and treating the representation theories of groups, Lie algebras, and quivers as special cases. Using this approach, the book covers a number of standard topics in the representation theories of these structures. Theoretical material in the book is supplemented by many problems and exercises which touch upon a lot of additional topics; the more difficult exercises are provided with hints. The book is designed as a textbook for advanced undergraduate and beginning graduate students. It should be accessible to students with a strong background in linear algebra and a basic knowledge of abstract algebra.

Eureka Math

Eureka Math
Author:
Publisher:
Total Pages:
Release: 2015
Genre: Algebra II
ISBN: 9781632553300

Eureka helps students to truly understand math, connect it to the real world, and prepare them to solve problems they haven’t encountered before. The team of teachers and mathematicians who created Eureka Math believe that it is not enough for students to know the process for solving a problem; they need to know why that process works. Eureka presents math as a story, one that develops from grades PK through 12. In A Story of Functions, our high school curriculum, this sequencing has joined with the methods of instruction that have been proven to work, in this nation and abroad.

The History of Mathematics

The History of Mathematics
Author: David M. Burton
Publisher: WCB/McGraw-Hill
Total Pages: 544
Release: 1985
Genre: Mathematics
ISBN: 9780697068552

"The History of Mathematics: An Introduction," Sixth Edition, is written for the one- or two-semester math history course taken by juniors or seniors, and covers the history behind the topics typically covered in an undergraduate math curriculum or in elementary schools or high schools. Elegantly written in David Burton's imitable prose, this classic text provides rich historical context to the mathematics that undergrad math and math education majors encounter every day. Burton illuminates the people, stories, and social context behind mathematics'greatest historical advances while maintaining appropriate focus on the mathematical concepts themselves. Its wealth of information, mathematical and historical accuracy, and renowned presentation make The History of Mathematics: An Introduction, Sixth Edition a valuable resource that teachers and students will want as part of a permanent library.

Connecting Abstract Algebra to Secondary Mathematics, for Secondary Mathematics Teachers

Connecting Abstract Algebra to Secondary Mathematics, for Secondary Mathematics Teachers
Author: Nicholas H. Wasserman
Publisher: Springer
Total Pages: 465
Release: 2018-12-12
Genre: Education
ISBN: 3319992147

Secondary mathematics teachers are frequently required to take a large number of mathematics courses – including advanced mathematics courses such as abstract algebra – as part of their initial teacher preparation program and/or their continuing professional development. The content areas of advanced and secondary mathematics are closely connected. Yet, despite this connection many secondary teachers insist that such advanced mathematics is unrelated to their future professional work in the classroom. This edited volume elaborates on some of the connections between abstract algebra and secondary mathematics, including why and in what ways they may be important for secondary teachers. Notably, the volume disseminates research findings about how secondary teachers engage with, and make sense of, abstract algebra ideas, both in general and in relation to their own teaching, as well as offers itself as a place to share practical ideas and resources for secondary mathematics teacher preparation and professional development. Contributors to the book are scholars who have both experience in the mathematical preparation of secondary teachers, especially in relation to abstract algebra, as well as those who have engaged in related educational research. The volume addresses some of the persistent issues in secondary mathematics teacher education in connection to advanced mathematics courses, as well as situates and conceptualizes different ways in which abstract algebra might be influential for teachers of algebra. Connecting Abstract Algebra to Secondary Mathematics, for Secondary Mathematics Teachers is a productive resource for mathematics teacher educators who teach capstone courses or content-focused methods courses, as well as for abstract algebra instructors interested in making connections to secondary mathematics.

Research Methods in Human Development

Research Methods in Human Development
Author: Paul C. Cozby
Publisher: WCB/McGraw-Hill
Total Pages: 300
Release: 1989
Genre: Psychology
ISBN:

For undergradute social science majors. A textbook on the interpretation and use of research. Annotation copyright Book News, Inc. Portland, Or.