MAA Problem Book Series

By

Rating

Product Description

Product Details

Foreword George Berzsenyi; Preface; List of winners; 1. Kurschak Mathematics Competition problems: 1947; 1948; 1949; 1950; 1951; 1952; 1953; 1954; 1955; 1957; 1958; 1959; 1960; 1961; 1962; 1963; Part II. Background: 2. Theorems in combinatorics; 3. Additional theorems in combinatorics; 4. Theorems in number theory; 5. Theorems in algebra; 6. Additional theorems in algebra; 7. Theorems in geometry; Part III. Solutions to Problems: 8. Problem set: combinatorics; 9. Problem set: graph theory; 10. Problem set: number theory; 11. Problem set: divisibility; 12. Problem set: sums and differences; 13. Problem set: algebra; 14. Problem set: geometry; 15. Problem set: tangent lines and circles; 16. Problem set: geometric inequalities; 17. Problem set: combinatorial geometry; 18. Problem set: trigonometry; 19. Problem set: solid geometry; Part IV. Looking Back: 20. Discussion on combinatorics; 21. Discussion on number theory; 22. Discussion on algebra; 23. Discussion on geometry; About the editors.

Forty-eight challenging problems from the oldest high school mathematics competition in the world.

Composed in a tradition that has enriched the experience of
countless young students with elementary mathematics through a
wealth of original problems that elicit creative thinking in
ingenious settings, Hungarian Problem Book IV is designed and
executed in such a way that does credit to, and in some ways
surpasses its origins. The translation and edition, begun by Robert
Barrington Leigh and Andy Liu and completed by the latter, of the
original Hungarian compilation of problems from the Kurschak
Competition of 1947 to 1963, is complemented by a carefully
constructed framework of results in algebra, geometry, number
theory and combinatorics that make it a self-contained resource for
study, contemplation and enjoyment. Here can be found problems that
have become classics in the literature of mathematical
competitions, as well as many not encountered in other collections
and that most readers will find both refreshing and intriguing.
Breadth is achieved not only by the topics spanned but also by
presenting many alternative solutions to each problem...
Additionally, George Berzsenyi's foreword is most informative,
setting, the scene perfectly. We most highly recommend to our
readers this new addition to an excellent series of publications
that comes to us from the MAA."" - Maria Falk de Losada

""World Federation of National Mathematics Competitions Every young
(or not so young) mathematician enjoys a good problem to ponder,
hence the popularity of mathematics competitions, ranging from
local in-school contests to international meetings where (a bit of)
national prestige is at stake. The oldest, and one of the most
famous, of these is the Hungarian mathematics competition
(Eotvos/Kurschak) held annually since 1894. This volume, published
by the MAA, collects the problems from this competition from 1947
to 1963 along with solutions and commentary. Since the competition
is for senior high school students the problems need less
mathematical background knowledge than, for example, the Putnam
competition problems and are concentrated mainly in combinatorics,
geometry and elementary number theory. The MAA has also published
collections of problems from earlier years (Volume 1, 1894 to 1905,
Volume 2, 1906 to 1928, Volume 3, 1929 to 1943) and it is an
interesting exercise to compare these to see how taste in the
choice of problems has evolved. The current volume contains
extensive commentary and alternative solutions for many of the
problems as well as valuable advice for students and coaches
preparing for similar competitions and concludes with an
interesting discussion of possible extensions of some of the
problems. This is a valuable resource which should be part of every
college and high school library."" -Keith Johnson, *CMS
Notes*

""Anticipated to widen the originality of elementary mathematics
problems and deepen the creativity and diversity of their
solutions, *Hungarian Problem Book IV* proves to be a
valuable tool for students interested in preparing for mathematics
competitions and for all those involved in organizing them. The
book is a precious collection of problems from the Kurschak
Mathematics Competition, which is the oldest high school
mathematics competition in the world. Robert Barrington Leigh and
Andy Liu have worked diligently in the translation of the original
48 problems from the Hungarian Kurschak Competition of 1947 to
1963, editing and organizing them by subject: combinatorics, graph
theory, number theory, divisibility, sums and difference, algebra,
geometry, tangent lines and circles, geometric inequalities,
combinatorial geometry, trigonometry and solid geometry. The
experienced reader will find some new and intriguing problems here.
*Hungarian Problem Book IV* is of course a sequel to
*Hungarian Problem Book III*. The latter discusses Polya's
four-step method for problem-solving, focusing mostly on the first
three steps (understanding the problem, making a plan, and carrying
out the plan). The final chapter of *Hungarian Problem Book
IV*, ""looking Back,"" illustrates the usage of the fourth step
in Polya's problem-solving process, which is looking back and
eliciting further insights into the problems. An example is the
discussion of problems in number theory. The authors begin by
proving that an integer can be expressed as the sum of two squares
if and only if twice that number can be so expressed. then he
deviates from this problem to another one, as he tries to determine
all positive integers m such that (m-1)! is divisible by m. He
draws the solution from Wilson's Theorem, and proves it using
geometric intuition. Next, he digresses once again to consider the
Fermat's Little Theorem (which is a result very close to Wilson's
Theorem) and proceeds to prove it. Finally, he explores Waring's
Problem and looks back at yet another related problem which
involves the Fermat Numbers. Thus this discussion exhibits an
astonishing interplay between results of the different problems.
The problems and their solutions draw on numerous famous theorems
and concepts; to name a few: Ramsey's Theorem, Hamiltonian cycles,
Farey fractions, Chebyshev's Inequality, Vieta's Formulae, Cantor's
Diagonalization Method, Hall's Theorem, Euler's formula, etc., all
of which are introduced and explained. *Hungarian Problem Book
IV* enriches its readers' problem-solving technique and
challenges their creative thinking."" - *MAA Reviews*

Ask a Question About this Product More... |

Look for similar items by category

People also searched for

How Fishpond Works

Fishpond works with suppliers all over the world to bring you a huge selection of products, really great prices, and delivery included on over 25 million products that we sell.
We do our best every day to make Fishpond an awesome place for customers to shop and get what they want — all at the best prices online.

Webmasters, Bloggers & Website Owners

You can earn a 5%
commission by selling MAA Problem Book Series: Hungarian Problem Book IV
on your website. It's easy to get started - we will give you example code.
After you're set-up, your website can earn you money while you work, play or even sleep!
You should start right now!

Authors / Publishers

Item ships from and is sold by Fishpond World Ltd.

↑

Back to top