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Calculus for Teachers: Whence Complex Numbers

By David Bressoud @dbressoud As of 2024, new Launchings columns appear on the third Tuesday of the month. Last month I tried to convey why complex numbers should be of interest to someone teaching regular real-valued calculus. This month I want to tackle an even more basic question: How did anybody even think to include the...

Mathematical Reflections – Two Lockdown Years

Although the authors primarily see this book, “encouraged by appreciative and constructive feedback from faithful readers, as a compilation and revision of the 2020 and 2021 volumes of the online journal, Mathematical Reflections", this reviewer would emphasize two other aspects of the book: i) a multi-national statement of human resilience in response to the pandemic, and ii) a collection of 16 beautiful...

Ten Themes in Algebra for Mathematics Competitions

This book reviews ten major techniques useful in solving mathematical problems. It should be of use to mathematics competition candidates, problem writers, problem solvers, and researchers. The book form facilitates mastery of these techniques: The first 40% of the book presents brief but concise exposition of theory accompanied by practice problems while the last 60%...

120 Awesome Algebra Problems

This book, employing a problem-solving approach, reviews useful algebraic techniques that many of us don’t think of initially. Therefore, this book should be of interest to those who prepare for Olympiad competitions, to mathematics researchers including student researchers, as well as to those who enjoy recreationally reading a good collection of problems solved by ingenious methods. This book...

Recurrent Sequences

What a delightful, current, compactly written book. This book could serve as a stand-alone text i) for an advanced, undergraduate, second-term, Discrete-Mathematics course, ii) for a first, or preferably, second-year stand-alone text for graduate students specializing in dynamical systems, combinatorics, or discrete systems, or iii) for researchers in these areas. The prerequisites for reading the book ...

Fractions: To Be Continued

This book presents the program of the Park City Math Institute during the summer 2018 which ran for two hours a day for three weeks. The focus that year was on Harmonic Analysis and the problems highlight connections with continuing fractions, the Euclidean algorithm, golden ratio, Pell equations, approximations of rational and irrational numbers as well as many...

Elements of Mathematics

The book Elements of Mathematics by Gabor Toth is a part of the series of undergraduate texts in mathematics published by Springer and designed for students studying mathematics at North American universities. The book aims at presenting rigorous theories before calculus is introduced. Transparency of explanation and gradually built material are outstanding features of the textbook. In addition,...

Mathematical Labyrinths. Pathfinding

This volume, the 22nd entry of World Scientific’s Problem Solving in Mathematics and Beyond series, will serve as an excellent resource for mathematics teachers, coaches of problem-solving teams, and anyone else who enjoys puzzling over clever problems, providing useful additions to a reader’s problem-solving toolkit. The book focuses on reasoning and problem analysis and contains many useful suggestions for...

Book cover of "Mathematical Labyrinths. Pathfinding" by Boris Pritsker. The design features a bright, yellow background and a graphic of a human head made of mathematical symbols and numbers in various colors. Under the title is a medium-sized, navy graphic of a labyrinth. At the bottom right corner is the name of the publisher, World Scientific.

Examples and Problems in Advanced Calculus: Real-Valued Functions

Examples and Problems in Advanced Calculus: Real-Valued Functions delivers exactly what it promises. The book provides a plethora of advanced problems across (real-valued) calculus. It primarily focuses on material covered in undergraduate Calculus 1 and in Real Analysis, with an emphasis on the latter. The text is split into topics, with each topic including a subsection...

Cover of 'Examples and Problems in Advanced Calculus: Real-Valued Functions' by Bijan Davvaz, featuring a minimalist design with the title and author's name prominently displayed on a solid background.

New, Newer, and Newest Inequalities

New, Newer and Newest Inequalities – a problem book from Titu Andreescu and Marius Stanean – is intended as a sequel to 116 Algebraic Inequalities From the Awesome Math Year-Round Program (2018) and 118 Inequalities for Mathematics Competitions (2019). Much like the previous two works also published by XYZ Press – a company founded in 2008 by famous head coach...

Cover of 'New, Newer, and Newest Inequalities' by Titu Andreescu and Marius Stanean, featuring a minimalist design with the title and authors' names prominently displayed on a solid background.