Constructing concise and correct proofs is one of the most challenging aspects of learning to work with advanced mathematics. Meeting this challenge is a defining moment for those considering a career in mathematics or related fields. Mathematical Thinking and Writing teaches readers to construct proofs and communicate with the precision necessary for working with abstraction. It is based on two premises: composing clear and accurate mathematical arguments is critical in abstract mathematics, and that this skill requires development and support. Abstraction is the destination, not the starting point.
Maddox methodically builds toward a thorough understanding of the proof process, demonstrating and encouraging mathematical thinking along the way. Skillful use of analogy clarifies abstract ideas. Clearly presented methods of mathematical precision provide an understanding of the nature of mathematics and its defining structure.
Mathematics educators agree that problem solving is one of the
essential skills their students should possess, yet few mathematics
courses or textbooks are devoted entirely to developing this skill.
Supported by narrative, examples, and exercises, Ants, Bikes, and
Clocks: Problem Solving for Undergraduates is a readable and enjoyable
text designed to strengthen the problem-solving skills of undergraduate
students. The book, which provides hundreds of mathematical problems,
gives special emphasis to problems in context, often called story
problems or modeling problems, that require mathematical formulation as
a preliminary step. Both analytical and computational approaches, as
well as the interplay between them, are included. This engaging book
will strengthen students' mathematical skills, introduce them to new
mathematical ideas, demonstrate the connectedness of mathematics, and
improve both their analytical and computational problem solving.
Students are encouraged to use the computer, or any tool at hand, for
experimentation or to test their ideas.
IQ Brainteasers is the ultimate test of your brain power. Packed with over 300 puzzles, your visual, mathematical and lateral-thinking abilities will be stretched to the limit.
Also included are some Japanese puzzles – Sudoku, Bridges and Slitherlink – which will really get your brain cells working.
Divided into puzzle types, the sections are not in any order of difficulty – you are just as likely to find two easy puzzles side-by-side as a more tricky one next to a simple one.
Some will require a degree of mathematical ability, others you just need to use your eyes, while others still will need some knowledge of words.
This is a partial record of the Bay Area Math Adventures (BAMA), a lecture series for high school students (and incidentally their teachers, parents, and other interested adults) hosted by San Jose State and Santa Clara Universities in the San Francisco Bay Area. These lectures are aimed primarily at talented high school students and as a result, the mathematics in some cases is far from what one would expect to see in talks at this level. There are serious mathematical issues addressed here. The authors are distinguished mathematicians; some are bright newcomers while others have been well known in mathematical circles for decades. We hope that this book will capture some of the magic of these talks that have filled auditoriums at the host schools almost monthly for several years. Join the students in sharing these mathematical adventures.
This book develops a theory of mathematics as a multi-semiotic discourse from the perspective of M. A. K. Halliday's systemic functional linguistics. From this perspective mathematical discourse is seen to involve the use of the three semiotic resources of language, visual images and mathematical symbolism. These semiotic resources are considered as functional sign systems which are organised grammatically. O'Halloran suggests that mathematical texts represent specific semiotic choices from the available grammatical systems. From this she articulates the ways in which a social semiotic perspective can inform mathematics teaching and learning.
