Conceptual Mathematics

Conceptual Mathematics
Author: F. William Lawvere
Publisher: Cambridge University Press
Total Pages: 409
Release: 2009-07-30
Genre: Mathematics
ISBN: 0521894859

This truly elementary book on categories introduces retracts, graphs, and adjoints to students and scientists.


Concept-Based Mathematics

Concept-Based Mathematics
Author: Jennifer T.H. Wathall
Publisher: Corwin Press
Total Pages: 307
Release: 2016-01-14
Genre: Education
ISBN: 150633265X

Give math students the connections between what they learn and how they do math—and suddenly math makes sense If your secondary-school students are fearful of or frustrated by math, it’s time for a new approach. When you teach concepts rather than rote processes, you show students math’s essential elegance, as well as its practicality—and help them discover their own natural mathematical abilities. This book is a road map to retooling how you teach math in a deep, clear, and meaningful way —through a conceptual lens—helping students achieve higher-order thinking skills. Jennifer Wathall shows you how to plan units, engage students, assess understanding, incorporate technology, and even guides you through an ideal concept-based classroom. Practical tools include: Examples from arithmetic to calculus Inquiry tasks, unit planners, templates, and activities Sample assessments with examples of student work Vignettes from international educators A dedicated companion website with additional resources, including a study guide, templates, exemplars, discussion questions, and other professional development activities. Everyone has the power to understand math. By extending Erickson and Lanning’s work on Concept-Based Curriculum and Instruction specifically to math, this book helps students achieve the deep understanding and skills called for by global standards and be prepared for the 21st century workplace. "Jennifer Wathall’s book is one of the most forward thinking mathematics resources on the market. While highlighting the essential tenets of Concept-Based Curriculum design, her accessible explanations and clear examples show how to move students to deeper conceptual understandings. This book ignites the mathematical mind!" — Lois A. Lanning, Author of Designing Concept-based Curriculum for English-Language Arts, K-12 "Wathall is a master at covering all the bases here; this book is bursting with engaging assessment examples, discussion questions, research, and resources that apply specifically to mathematical topics. Any math teacher or coach would be hard-pressed to read it and not come away with scores of ideas, assessments, and lessons that she could use instantly in the classroom. As an IB Workshop Leader and instructional coach, I want this book handy on a nearby shelf for regular referral – it′s a boon to any educator who wants to bring math to life for students." — Alexis Wiggins, Instructional Coach, IB Workshop Leader and Consultant


How We Understand Mathematics

How We Understand Mathematics
Author: Jacek Woźny
Publisher: Springer
Total Pages: 122
Release: 2018-04-25
Genre: Mathematics
ISBN: 3319776886

This volume examines mathematics as a product of the human mind and analyzes the language of "pure mathematics" from various advanced-level sources. Through analysis of the foundational texts of mathematics, it is demonstrated that math is a complex literary creation, containing objects, actors, actions, projection, prediction, planning, explanation, evaluation, roles, image schemas, metonymy, conceptual blending, and, of course, (natural) language. The book follows the narrative of mathematics in a typical order of presentation for a standard university-level algebra course, beginning with analysis of set theory and mappings and continuing along a path of increasing complexity. At each stage, primary concepts, axioms, definitions, and proofs will be examined in an effort to unfold the tell-tale traces of the basic human cognitive patterns of story and conceptual blending. This book will be of interest to mathematicians, teachers of mathematics, cognitive scientists, cognitive linguists, and anyone interested in the engaging question of how mathematics works and why it works so well.


Sets for Mathematics

Sets for Mathematics
Author: F. William Lawvere
Publisher: Cambridge University Press
Total Pages: 280
Release: 2003-01-27
Genre: Mathematics
ISBN: 9780521010603

In this book, first published in 2003, categorical algebra is used to build a foundation for the study of geometry, analysis, and algebra.


A Concept of Limits

A Concept of Limits
Author: Donald W. Hight
Publisher: Courier Corporation
Total Pages: 164
Release: 2012-07-17
Genre: Mathematics
ISBN: 0486153126

An exploration of conceptual foundations and the practical applications of limits in mathematics, this text offers a concise introduction to the theoretical study of calculus. Many exercises with solutions. 1966 edition.


Elementary Concepts of Topology

Elementary Concepts of Topology
Author: Paul Alexandroff
Publisher: Courier Corporation
Total Pages: 68
Release: 2012-08-13
Genre: Mathematics
ISBN: 0486155064

Concise work presents topological concepts in clear, elementary fashion, from basics of set-theoretic topology, through topological theorems and questions based on concept of the algebraic complex, to the concept of Betti groups. Includes 25 figures.


New Spaces in Mathematics: Volume 1

New Spaces in Mathematics: Volume 1
Author: Mathieu Anel
Publisher: Cambridge University Press
Total Pages: 602
Release: 2021-04-01
Genre: Mathematics
ISBN: 1108848214

After the development of manifolds and algebraic varieties in the previous century, mathematicians and physicists have continued to advance concepts of space. This book and its companion explore various new notions of space, including both formal and conceptual points of view, as presented by leading experts at the New Spaces in Mathematics and Physics workshop held at the Institut Henri Poincaré in 2015. The chapters in this volume cover a broad range of topics in mathematics, including diffeologies, synthetic differential geometry, microlocal analysis, topos theory, infinity-groupoids, homotopy type theory, category-theoretic methods in geometry, stacks, derived geometry, and noncommutative geometry. It is addressed primarily to mathematicians and mathematical physicists, but also to historians and philosophers of these disciplines.


The Concept of a Riemann Surface

The Concept of a Riemann Surface
Author: Hermann Weyl
Publisher: Courier Corporation
Total Pages: 210
Release: 2013-12-31
Genre: Mathematics
ISBN: 048613167X

This classic on the general history of functions combines function theory and geometry, forming the basis of the modern approach to analysis, geometry, and topology. 1955 edition.


Mathematics for Elementary Teachers

Mathematics for Elementary Teachers
Author: Albert B. Bennett
Publisher: McGraw-Hill Science, Engineering & Mathematics
Total Pages: 0
Release: 2007
Genre: Mathematics
ISBN: 9780073053707

This book is designed for a mathematics for elementary school teachers course where instructors choose to focus on and/or take an activities approach to learning. It provides inductive activities for prospective elementary school teachers and incorporates the use of physical models, manipulatives, and visual images to develop concepts and encourage higher-level thinking. This text contains an activity set that corresponds to each section of the companion text, Mathematics for Elementary Teachers: A Conceptual Approach which is also by Bennett/Nelson. The Activities Approach text can be used independently or along with its companion volume. The authors are pleased to welcome Laurie Burton, PhD, Western Oregon University to this edition of Mathematics for Elementary Teachers: An Activity Approach.