math olympiad book

Sums and Products

$ 44.95

Take your understanding of sums and products to the outer limits with solid theory and rich examples. Students who wish to participate in mathematics competitions at the AIME and USAMO levels, their teachers, as well as for all who have a fire for mathematics, will greatly benefit from Sums and Products.
SKU: XYZ-1051 Category:

The main areas covered are:

  • Telescoping sums and products in algebra and trigonometry
  • The use of complex numbers and de Moivre’s Formula
  • Abel’s summation formula
  • Mathematical induction
  • Combinatorial identities
  • Multiplicative functions and the use of M¨obius function.
The theory is presented together with rich examples. At the end, you are invited to solve problems from a list of 125 questions divided into three levels.

Authors

  • Titu Andreescu and Marian Tetiva

Subjects

  • Algebra
  • Trigonometry
  • Number Theory
  • Combinatorics

Book Details

  • Hardcover: 340 pages
  • Publisher: XYZ Press (2018)
  • Language: English
  • ISBN-10: 0-9993428-1-9
  • ISBN-13: 978-0-9993428-1-7
alt: sums-and-products-look-inside.pdf

I have been using this book as my go to text in practicing summation problems for the William Lowell Putnam competition. The text contains a rich set of fully-worked problems ranging from telescoping sums to applications of sums and products in number theory and combinatorics. The authors include well-written proofs of engaging problems that demonstrate how different problem solving techniques work; but more importantly there is very good commentary on why a certain technique was chosen to solve a problem. Truly an invaluable resource for all levels of math competitors.

Caiden P. (Kansas)

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