problem solving through problems larson

Problem-Solving Through Problems

• © 1983
• Loren C. Larson 0

Department of Mathematics, St. Olaf College, Northfield, USA

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Part of the book series: Problem Books in Mathematics (PBM)

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Problem Solving

That Most Important Intersection

Commentary on Part III of Mathematical Challenges For All: On Problems, Problem-Solving, and Thinking Mathematically

• Cauchy-Schwarz Inequality
• Problem solving
• Schwarz inequality
• fundamental theorem
• mean value theorem
• pigeonhole principle

Table of contents (8 chapters)

Front matter.

Loren C. Larson

Two Important Principles: Induction and Pigeonhole

Summation of series, intermediate real analysis, inequalities, back matter, authors and affiliations, bibliographic information.

Book Title : Problem-Solving Through Problems

Authors : Loren C. Larson

Series Title : Problem Books in Mathematics

DOI : https://doi.org/10.1007/978-1-4612-5498-0

Publisher : Springer New York, NY

eBook Packages : Springer Book Archive

Copyright Information : Springer-Verlag New York Inc. 1983

Softcover ISBN : 978-0-387-96171-2 Published: 17 July 1985

eBook ISBN : 978-1-4612-5498-0 Published: 06 December 2012

Series ISSN : 0941-3502

Series E-ISSN : 2197-8506

Edition Number : 1

Number of Pages : XI, 352

Number of Illustrations : 11 b/w illustrations

Topics : Analysis , Mathematics, general

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Problem-Solving Through Problems (Problem Books in Mathematics)

Description.

Problem-Solving Through Problems is a practical anthology of some of the best elementary problems in different branches of mathematics. This classroom tested material will teach its readers 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.

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Problem-Solving Through Problems Paperback – Illustrated, July 17 1985

Purchase options and add-ons.

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.

• ISBN-10 0387961712
• ISBN-13 978-0387961712
• Edition 1st ed. 1983. Corr. 3rd printing 1992
• Publisher Springer
• Publication date July 17 1985
• Part of series Problem Books in Mathematics
• Language English
• Dimensions 15.49 x 2.03 x 23.5 cm
• Print length 363 pages
• See all details

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From the reviews:

"This is a very welcome addition. The main message of the book is that the only way to learn to solve problems is to solve problems! I found this book very helpful. I am quite sure the book will be in constant use and I have no hesitation in recommending it." (The Mathematical Gazette)

Product details

• Publisher ‏ : ‎ Springer; 1st ed. 1983. Corr. 3rd printing 1992 edition (July 17 1985)
• Language ‏ : ‎ English
• Paperback ‏ : ‎ 363 pages
• ISBN-10 ‏ : ‎ 0387961712
• ISBN-13 ‏ : ‎ 978-0387961712
• Item weight ‏ : ‎ 1.09 kg
• Dimensions ‏ : ‎ 15.49 x 2.03 x 23.5 cm
• #244 in Mathematical Analysis Books
• #376 in Mathematical Analysis (Books)
• #439 in Science Dictionaries

About the author

Loren c larson.

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Problem-Solving Through Problems Paperback – 17 July 1985

Purchase options and add-ons.

• Part of series Problem Books in Mathematics
• Print length 363 pages
• Language English
• Publisher Springer
• Publication date 17 July 1985
• Dimensions 15.49 x 2.03 x 23.5 cm
• ISBN-10 0387961712
• ISBN-13 978-0387961712
• See all details

Frequently bought together

Customers who viewed this item also viewed

Product description

From the reviews:

"This is a very welcome addition. The main message of the book is that the only way to learn to solve problems is to solve problems! I found this book very helpful. I am quite sure the book will be in constant use and I have no hesitation in recommending it." (The Mathematical Gazette)

Product details

• Publisher ‏ : ‎ Springer; 1983rd edition (17 July 1985)
• Language ‏ : ‎ English
• Paperback ‏ : ‎ 363 pages
• ISBN-10 ‏ : ‎ 0387961712
• ISBN-13 ‏ : ‎ 978-0387961712
• Dimensions ‏ : ‎ 15.49 x 2.03 x 23.5 cm
• 548 in Mathematical Analysis (Books)
• 1,155 in Pure Mathematics (Books)
• 313,242 in Textbooks & Study Guides

About the author

Loren c larson.

Discover more of the author’s books, see similar authors, read author blogs, and more

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Larson: Chapter 1 problems

Here is a selection of problems from the first chapter of Larson's "Problem-solving through problems", 1983 edition:

• Read the comments at the beginning of each section - they describe the method.
• Section 1.1, Search for a patern: 1.1.1, 1.1.2, 1.1.5, 1.1.6 (write enough terms!), 1.1.9 (i.e., count mod 2), 1.1.11
• Section 1.2, Draw a figure: 1.2.3; 1.2.6 - 1.2.9
• Section 1.3, Formulate an equivalent problem: 1.3.2, 1.3.4; 1.3.8, 1.3.11
• Section 1.4, Modify the problem: 1.4.1, 1.4.4 (you probably saw this in Calculus III)
• Section 1.5, Choose effective notation: 1.5.1 (this is in the Math 2431 textbook), 1.5.3, 1.5.4; 1.5.7, 1.5.9
• Section 1.6, Exploit symmetry: comments before and after 1.6.1, 1.6.2, 1.6.4 (fill in the details); 1.6.8
• Section 1.7, Divide into cases: 1.7.2, 1.7.3; 1.7.5 (no need to look at "cases" if you use the correct approach!), 1.7.7, 1.7.8 (Hint: play with 0, 1, x .)
• Section 1.8, Work backward: the introductory example, 1.8.1, 1.8.2 (although it does not matter for this problem, note that three numbers a, b, c are the sides of a triangle if and only if a=x+y, b=y+z, c=x+z with x, y, z > 0 ; one proof is to look at the inscribed circle) 1.8.4; 1.8.5 (Typo: in part (b) replace the 2 in the LHS by 1 .), 1.8.8
• Section 1.9, Argue by contradiction: introductory remarks, 1.9.2; 1.9.2, 1.9.3
• Section 1.10, Pursue parity: 1.10.1, 1.10.2; 1.10.6, 1.10.7, 1.10.8, 1.10.10
• Section 1.11, Consider extreme cases: 1.11.1, 1.11.2, 1.11.4; 1.11.6. 1.11.8
• Section 1.12, Generalize: 1.12.1, 1.12.2, 1.12.3; 1.12.5, 1.12.7