Advanced Problems in Mathematics
Advanced Problems in Mathematics

Author: Stephen Siklos

Publisher:

Published: 2019-10-16

Total Pages: 188

ISBN-13: 9781783747764

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This new and expanded edition is intended to help candidates prepare for entrance examinations in mathematics and scientific subjects, including STEP (Sixth Term Examination Paper). STEP is an examination used by Cambridge Colleges for conditional offers in mathematics. They are also used by some other UK universities and many mathematics departments recommend that their applicants practice on the past papers even if they do not take the examination. Advanced Problems in Mathematics bridges the gap between school and university mathematics, and prepares students for an undergraduate mathematics course. The questions analysed in this book are all based on past STEP questions and each question is followed by a comment and a full solution. The comments direct the reader's attention to key points and put the question in its true mathematical context. The solutions point students to the methodology required to address advanced mathematical problems critically and independently. This book is a must read for any student wishing to apply to scientific subjects at university level and for anyone interested in advanced mathematics.

Advanced Mathematics
Advanced Mathematics

Author: Stanley J. Farlow

Publisher: John Wiley & Sons

Published: 2019-09-19

Total Pages: 475

ISBN-13: 1119563488

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Provides a smooth and pleasant transition from first-year calculus to upper-level mathematics courses in real analysis, abstract algebra and number theory Most universities require students majoring in mathematics to take a “transition to higher math” course that introduces mathematical proofs and more rigorous thinking. Such courses help students be prepared for higher-level mathematics course from their onset. Advanced Mathematics: A Transitional Reference provides a “crash course” in beginning pure mathematics, offering instruction on a blendof inductive and deductive reasoning. By avoiding outdated methods and countless pages of theorems and proofs, this innovative textbook prompts students to think about the ideas presented in an enjoyable, constructive setting. Clear and concise chapters cover all the essential topics students need to transition from the "rote-orientated" courses of calculus to the more rigorous "proof-orientated” advanced mathematics courses. Topics include sentential and predicate calculus, mathematical induction, sets and counting, complex numbers, point-set topology, and symmetries, abstract groups, rings, and fields. Each section contains numerous problems for students of various interests and abilities. Ideally suited for a one-semester course, this book: Introduces students to mathematical proofs and rigorous thinking Provides thoroughly class-tested material from the authors own course in transitioning to higher math Strengthens the mathematical thought process of the reader Includes informative sidebars, historical notes, and plentiful graphics Offers a companion website to access a supplemental solutions manual for instructors Advanced Mathematics: A Transitional Reference is a valuable guide for undergraduate students who have taken courses in calculus, differential equations, or linear algebra, but may not be prepared for the more advanced courses of real analysis, abstract algebra, and number theory that await them. This text is also useful for scientists, engineers, and others seeking to refresh their skills in advanced math.

Advanced Engineering Mathematics
Advanced Engineering Mathematics

Author: Michael Greenberg

Publisher:

Published: 2013-09-20

Total Pages: 1344

ISBN-13: 9781292042541

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Appropriate for one- or two-semester Advanced Engineering Mathematics courses in departments of Mathematics and Engineering. This clear, pedagogically rich book develops a strong understanding of the mathematical principles and practices that today's engineers and scientists need to know. Equally effective as either a textbook or reference manual, it approaches mathematical concepts from a practical-use perspective making physical applications more vivid and substantial. Its comprehensive instructional framework supports a conversational, down-to-earth narrative style offering easy accessibility and frequent opportunities for application and reinforcement.

The 'Resource' Approach to Mathematics Education
The 'Resource' Approach to Mathematics Education

Author: Luc Trouche

Publisher: Springer Nature

Published: 2019-11-29

Total Pages: 564

ISBN-13: 303020393X

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This edited volume will help educators better analyze methodological and practical tools designed to aid classroom instruction. It features papers that explore the need to create a system in order to fully meet the uncertainties and developments of modern educational phenomena. These have emerged due to the abundance of digital resources and new forms of collective work. The collected papers offer new perspectives to a rising field of research known as the Documentational Approach to Didactics. This framework was first created by the editors of this book. It seeks to develop a deeper understanding of mathematics teaching expertise. Readers will gain insight into how to meet the theoretical questions brought about by digitalization. These include: how to analyze teachers’ work when they prepare for their teaching, how to conceptualize the relationships between individual and collective work, and how to follow the related processes over the long term. The contributors also provide a comparative view in terms of contrasting selected phenomena across different educational cultures and education systems. For instance, they consider how differences in curriculum resources are available to teachers and how teachers make use of them to shape instruction. Coverage also considers the extent to which teachers make use of additional material, particularly those available through the global marketplace on the Internet. This book builds on works from the Re(s)sources 2018 Conference, Understanding teachers’ work through their interactions with resources for teaching, held in Lyon, France.

Advanced Mathematical Methods
Advanced Mathematical Methods

Author: Francesco Mainardi

Publisher: MDPI

Published: 2020-02-05

Total Pages: 198

ISBN-13: 3039282468

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The many technical and computational problems that appear to be constantly emerging in various branches of physics and engineering beg for a more detailed understanding of the fundamental mathematics that serves as the cornerstone of our way of understanding natural phenomena. The purpose of this Special Issue was to establish a brief collection of carefully selected articles authored by promising young scientists and the world's leading experts in pure and applied mathematics, highlighting the state-of-the-art of the various research lines focusing on the study of analytical and numerical mathematical methods for pure and applied sciences.

The Five Practices in Practice [Elementary]
The Five Practices in Practice [Elementary]

Author: Margaret (Peg) Smith

Publisher: Corwin Press

Published: 2019-08-14

Total Pages: 241

ISBN-13: 1544321147

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Take a deep dive into the five practices for facilitating productive mathematical discussions Enhance your fluency in the five practices—anticipating, monitoring, selecting, sequencing, and connecting—to bring powerful discussions of mathematical concepts to life in your elementary classroom. This book unpacks the five practices for deeper understanding and empowers you to use each practice effectively. • Video excerpts vividly illustrate the five practices in action in real elementary classrooms • Key questions help you set learning goals, identify high-level tasks, and jumpstart discussion • Prompts guide you to be prepared for and overcome common challenges Includes planning templates, sample lesson plans and completed monitoring tools, and mathematical tasks.

Elementary Mathematical Models: An Accessible Development without Calculus, Second Edition
Elementary Mathematical Models: An Accessible Development without Calculus, Second Edition

Author: Dan Kalman

Publisher: American Mathematical Soc.

Published: 2019-08-02

Total Pages: 528

ISBN-13: 1470450011

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Elementary Mathematical Models offers instructors an alternative to standard college algebra, quantitative literacy, and liberal arts mathematics courses. Presuming only a background of exposure to high school algebra, the text introduces students to the methodology of mathematical modeling, which plays a role in nearly all real applications of mathematics. A course based on this text would have as its primary goal preparing students to be competent consumers of mathematical modeling in their future studies. Such a course would also provide students with an understanding of the modeling process and a facility with much of the standard, non-trigonometric, content of college algebra and precalculus. This book builds, successively, a series of growth models defined in terms of simple recursive patterns of change corresponding to arithmetic, quadratic, geometric, and logistic growth. Students discover and come to understand linear, polynomial, exponential, and logarithmic functions in the context of analyzing these models of intrinsically—and scientifically—interesting phenomena including polar ice extent, antibiotic resistance, and viral internet videos. Students gain a deep appreciation for the power and limitations of mathematical modeling in the physical, life, and social sciences as questions of modeling methodology are carefully and constantly addressed. Realistic examples are used consistently throughout the text, and every topic is illustrated with models that are constructed from and compared to real data. The text is extremely attractive and the exposition is extraordinarily clear. The lead author of this text is the recipient of nine MAA awards for expository writing including the Ford, Evans, Pólya, and Allendoerfer awards and the Beckenbach Book prize. Great care has been taken by accomplished expositors to make the book readable by students. Those students will also benefit from more than 1,000 carefully crafted exercises.

Advances in Mathematics Education Research on Proof and Proving
Advances in Mathematics Education Research on Proof and Proving

Author: Andreas J. Stylianides

Publisher: Springer

Published: 2018-01-10

Total Pages: 298

ISBN-13: 3319709968

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This book explores new trends and developments in mathematics education research related to proof and proving, the implications of these trends and developments for theory and practice, and directions for future research. With contributions from researchers working in twelve different countries, the book brings also an international perspective to the discussion and debate of the state of the art in this important area. The book is organized around the following four themes, which reflect the breadth of issues addressed in the book: • Theme 1: Epistemological issues related to proof and proving; • Theme 2: Classroom-based issues related to proof and proving; • Theme 3: Cognitive and curricular issues related to proof and proving; and • Theme 4: Issues related to the use of examples in proof and proving. Under each theme there are four main chapters and a concluding chapter offering a commentary on the theme overall.

A Transition to Advanced Mathematics
A Transition to Advanced Mathematics

Author: Douglas Smith

Publisher: Cengage Learning

Published: 2010-06-01

Total Pages: 416

ISBN-13: 9780495562023

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A TRANSITION TO ADVANCED MATHEMATICS helps students make the transition from calculus to more proofs-oriented mathematical study. The most successful text of its kind, the 7th edition continues to provide a firm foundation in major concepts needed for continued study and guides students to think and express themselves mathematically to analyze a situation, extract pertinent facts, and draw appropriate conclusions. The authors place continuous emphasis throughout on improving students' ability to read and write proofs, and on developing their critical awareness for spotting common errors in proofs. Concepts are clearly explained and supported with detailed examples, while abundant and diverse exercises provide thorough practice on both routine and more challenging problems. Students will come away with a solid intuition for the types of mathematical reasoning they'll need to apply in later courses and a better understanding of how mathematicians of all kinds approach and solve problems. Important Notice: Media content referenced within the product description or the product text may not be available in the ebook version.