Mathematical Concepts

Mathematical Concepts
Author: Jürgen Jost
Publisher: Springer
Total Pages: 315
Release: 2015-09-10
Genre: Mathematics
ISBN: 331920436X

The main intention of this book is to describe and develop the conceptual, structural and abstract thinking of mathematics. Specific mathematical structures are used to illustrate the conceptual approach; providing a deeper insight into mutual relationships and abstract common features. These ideas are carefully motivated, explained and illustrated by examples so that many of the more technical proofs can be omitted. The book can therefore be used: · simply as an overview of the panorama of mathematical structures and the relations between them, to be supplemented by more detailed texts whenever you want to acquire a working knowledge of some structure · by itself as a first introduction to abstract mathematics · together with existing textbooks, to put their results into a more general perspective · to gain a new and hopefully deeper perspective after having studied such textbooks Mathematical Concepts has a broader scope and is less detailed than standard mathematical textbooks so that the reader can readily grasp the essential concepts and ideas for individual needs. It will be suitable for advanced mathematicians, postgraduate students and for scientists from other fields with some background in formal reasoning.

What is a Mathematical Concept?

What is a Mathematical Concept?
Author: Elizabeth de Freitas
Publisher: Cambridge University Press
Total Pages: 301
Release: 2017-06-22
Genre: Education
ISBN: 1107134633

Leading thinkers in mathematics, philosophy and education offer new insights into the fundamental question: what is a mathematical concept?

Concepts of Modern Mathematics

Concepts of Modern Mathematics
Author: Ian Stewart
Publisher: Courier Corporation
Total Pages: 367
Release: 2012-05-23
Genre: Mathematics
ISBN: 0486134954

In this charming volume, a noted English mathematician uses humor and anecdote to illuminate the concepts of groups, sets, subsets, topology, Boolean algebra, and other mathematical subjects. 200 illustrations.

Evolution of Mathematical Concepts

Evolution of Mathematical Concepts
Author: Raymond L. Wilder
Publisher: Courier Corporation
Total Pages: 242
Release: 2013-01-01
Genre: Mathematics
ISBN: 0486490610

Accessible to students and relevant to specialists, this remarkable book by a prominent educator offers a unique perspective on the evolutionary development of mathematics. Rather than conducting a survey of the history or philosophy of mathematics, Raymond L. Wilder envisions mathematics as a broad cultural phenomenon. His treatment examines and illustrates how such concepts as number and length were affected by historic and social events. Starting with a brief consideration of preliminary notions, this study explores the early evolution of numbers, the evolution of geometry, and the conquest of the infinite as embodied by real numbers. A detailed look at the processes of evolution concludes with an examination of the evolutionary aspects of modern mathematics.

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

Mathematical Concepts and Methods in Modern Biology

Mathematical Concepts and Methods in Modern Biology
Author: Raina Robeva
Publisher: Academic Press
Total Pages: 372
Release: 2013-02-26
Genre: Mathematics
ISBN: 0124157939

Mathematical Concepts and Methods in Modern Biology offers a quantitative framework for analyzing, predicting, and modulating the behavior of complex biological systems. The book presents important mathematical concepts, methods and tools in the context of essential questions raised in modern biology. Designed around the principles of project-based learning and problem-solving, the book considers biological topics such as neuronal networks, plant population growth, metabolic pathways, and phylogenetic tree reconstruction. The mathematical modeling tools brought to bear on these topics include Boolean and ordinary differential equations, projection matrices, agent-based modeling and several algebraic approaches. Heavy computation in some of the examples is eased by the use of freely available open-source software. Features self-contained chapters with real biological research examples using freely available computational tools Spans several mathematical techniques at basic to advanced levels Offers broad perspective on the uses of algebraic geometry/polynomial algebra in molecular systems biology

Concepts of Mathematical Modeling

Concepts of Mathematical Modeling
Author: Walter J. Meyer
Publisher: Courier Corporation
Total Pages: 450
Release: 2012-10-23
Genre: Mathematics
ISBN: 0486137244

Appropriate for undergraduate and graduate students, this text features independent sections that illustrate the most important principles of mathematical modeling, a variety of applications, and classic models. Students with a solid background in calculus and some knowledge of probability and matrix theory will find the material entirely accessible. The range of subjects includes topics from the physical, biological, and social sciences, as well as those of operations research. Discussions cover related mathematical tools and the historical eras from which the applications are drawn. Each section is preceded by an abstract and statement of prerequisites, and answers or hints are provided for selected exercises. 1984 edition.

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.

Illustrating Mathematics

Illustrating Mathematics
Author: Diana Davis
Publisher: American Mathematical Soc.
Total Pages: 171
Release: 2020-10-16
Genre: Education
ISBN: 1470461226

This book is for anyone who wishes to illustrate their mathematical ideas, which in our experience means everyone. It is organized by material, rather than by subject area, and purposefully emphasizes the process of creating things, including discussions of failures that occurred along the way. As a result, the reader can learn from the experiences of those who came before, and will be inspired to create their own illustrations. Topics illustrated within include prime numbers, fractals, the Klein bottle, Borromean rings, tilings, space-filling curves, knot theory, billiards, complex dynamics, algebraic surfaces, groups and prime ideals, the Riemann zeta function, quadratic fields, hyperbolic space, and hyperbolic 3-manifolds. Everyone who opens this book should find a type of mathematics with which they identify. Each contributor explains the mathematics behind their illustration at an accessible level, so that all readers can appreciate the beauty of both the object itself and the mathematics behind it.

What is a Mathematical Concept?

What is a Mathematical Concept?
Author: Elizabeth de Freitas
Publisher: Cambridge University Press
Total Pages: 301
Release: 2017-06-22
Genre: Psychology
ISBN: 1108210783

Responding to widespread interest within cultural studies and social inquiry, this book addresses the question 'what is a mathematical concept?' using a variety of vanguard theories in the humanities and posthumanities. Tapping historical, philosophical, sociological and psychological perspectives, each chapter explores the question of how mathematics comes to matter. Of interest to scholars across the usual disciplinary divides, this book tracks mathematics as a cultural activity, drawing connections with empirical practice. Unlike other books in this area, it is highly interdisciplinary, devoted to exploring the ontology of mathematics as it plays out in different contexts. This book will appeal to scholars who are interested in particular mathematical habits - creative diagramming, structural mappings, material agency, interdisciplinary coverings - that shed light on both mathematics and other disciplines. Chapters are also relevant to social sciences and humanities scholars, as each offers philosophical insight into mathematics and how we might live mathematically.