Comments, suggestions, feedback, criticism all welcome.
Here is an initial list to get started. Note that AMT = Australian Mathematics Trust. As far as I know, its books are only available from its website (order by email). Similarly, MAA = Mathemacial Association of America. Some of its books are only available from its website.
Books on Elementary Mathematics |
Olympiad etc problem sets |
Training books, other problem sets |
|
| Greitzer, IMO 1959-1977, MAA 1978 | Martin Aigner, Günter M Ziegler, Proofs from the Book, 2nd ed, Springer 2001, ISBN 3540678654 (magical collection of elegant proofs) | |
| M S Klamkin, IMO 1978-1985, MAA 1986, ISBN 088386631X | Andreescu, Feng, 102 Combinatorial Problems, From the training of the USA IMO team, Birkhäuser 2003, ISBN 0817643176 Comments | |
| Andreescu, Kedlaya, Zeitz, Mathematical Contests 1995-1996: Olympiad problems from around the world, with solutions, AMC 1997. Available only from Mathematical Association of America. | Andreescu & Gelca, Mathematical Olympiad Challenges, Birkhäuser 2000, ISBN 0817641556 (general training book) Comments | |
| Andreescu, Kedlaya, Mathematical Contests 1996-1997: Olympiad problems from around the world, with solutions, AMC 1998. pdf 0.9Mb | Alan Baker, A concise introduction to the theory of numbers, Cambridge 1984, ISBN 0521286549 (more advanced than is needed) | |
| Andreescu, Kedlaya, Mathematical Contests 1997-1998: Olympiad problems from around the world, with solutions, AMC 1999. pdf 0.8Mb | Chen Chuan-Chong & Koh Khee-Meng, Principles and Techniques in Combinatorics, World Scientific 1992, ISBN 9810211392 (written by two people involved in training the Singapore IMO team) | |
| Andreescu, Feng, Mathematical Olympiads: Olympiad problems from around the world, 1998-1999, MAA 2000. ISBN 0883858037 | H S M Coxeter, S L Greitzer, Geometry Revisited, MAA 1967, ISBN 0883856190 | |
| Andreescu, Feng, Mathematical Olympiads: Olympiad problems from around the world, 1999-2000, MAA 2000. ISBN 0883858053 | Arthur Engel, Problem-solving strategies, Springer 1998, ISBN 0387982191 (olympiad training book) Comments | |
| A M Slinko, USSR Mathematical Olympiads 1989-1992, AMT 1997, ISBN 0646336185 (All Soviet Union Olympiads 1989-1992) | Dmitri Fomin, Sergey Genkin, Ilia Itenberg, Mathematical circles (Russian experience), AMS 1996, ISBN 0821804308 | |
| Lausch, Bosch Giral, Asian Pacific Mathematics Olympiads 1989-2000, AMT 1994, ISBN 1876420111 | Martin Gardner, The colossal book of mathematics, Norton 2001, ISBN 0393020231 (a selection of 50 of his best Scientific American columns, with updates) | |
| Lausch, Taylor, Australian Mathematical Olympiads 1979-1995, AMT 1997, ISBN 0858896451 | George T Gilbert, Mark I Krusemeyer & Loren C Larson, The Wohascum county problem book, MAA 1993, ISBN 0883853167 (a Putnam training book) | |
| M Kuczma, 144 problems of the Austrian-Polish Mathematics Competition 1978-1993 | Hadwiger, Debrunner, Klee, Combinatorial geometry in the plane, Holt Rinehart & Winston 1964 | |
| A Gardiner, The Mathematical Olympiad Handbook, Oxford 1997, ISBN 0198501056 (British Mathematical Olympiad 1965-1996) | Kenneth Hardy & Kenneth S Williams, The green book of mathematical problems, Dover 1985, ISBN 0486695735 (training book for the Putnam) | |
| Andy Liu, Chinese Mathematics Competitions and Olympiads 1981-1993, AMT 1998, ISBN 1876420006 | Kenneth S Williams & Kenneth Hardy, The red book of mathematical problems, Dover 1988, ISBN 0486694151 (training book for the Putnam) | |
| Kürshák, Hájos, Neukomm, Surányi, Hungarian Problem Book I, MAA 1967 (Eötvös Competition 1894-1905) | Littlewood's miscellany (ed Béla Bollobás), Cambridge 1953-1986, ISBN 052133702X (some material is more advanced, but an absolutely charming book) | |
| Kürshák, Hájos, Neukomm, Surányi, Hungarian Problem Book II, MAA 1967 (Eötvös Competition 1906-1928) | Donald J Newman, A problem seminar, Springer 1982, ISBN 0387907653 | |
| Andy Liu, Hungarian Problem Book III, MAA 2001 (Eötvös Competition 1929-1943), ISBN 0883856441 | G Pólya & G Szegö, Problems and theorems in analysis I, Springer 1972, ISBN 3540056726 (this and part II are probably the most famous problem books of all time, most parts require some knowledge of complex analysis - intended as an intro to research) | |
| Dmitry Fomin, Alexey Kirichenko, Leningrad Mathematical Olympiads 1987-1991, MathPro Press 1994, ISBN 096264014X | G Pólya & G Szegö, Problems and theorems in analysis II, Springer 1976, ISBN 3540069720 | |
| Shklarsky, Chentzov, Yaglom, The USSR Olympiad Problem Book, Dover 1962, ISBN 0486277097 (Selected Moscow Olympiad problems, and other problems) | Alfred S Posamentier, Charles T Salkind, Challenging problems in geometry, Dover 1970-88, ISBN 0486691543 | |
| Gábor J Székely, Contests in Higher Mathematics, Springer 1996, ISBN 0387945881 (Miklós Schweitzer Competitions 1962-1991) | ed Chris Pritchard, The changing shape of geometry, Cambridge 2003, ISBN 0521531624 (a splendid collection of articles on elementary geometry - no problems as such, but plenty of theorems) | |
| M Aassila, 300 défis mathématiques, Ellipses 2001, ISBN 272980840X (300 IMO shortlist problems and solutions) | Hans Rademacher & Otto Toeplitz, The enjoyment of mathematics, Dover (orig Princeton 1957), ISBN 0486262421 (almost a problem book) | |
| Taylor, Tournament of the Towns 1980-1984, AMT 1993 | Svetoslav Savchev & Titu Andreescu, Mathematical Miniatures, MAA 2003, ISBN 088385645X (an olympiad training book - 50 chapters, each a short olympiad topic + 9 "coffee breaks" (sets of 3 problems) ) | |
| Taylor, Tournament of the Towns 1984-1989, AMT 1992 | Hugo Steinhaus, One hundred problems in elementary mathematics, Dover 1964, ISBN 048623875X | |
| Taylor, Tournament of the Towns 1989-1993, AMT 1994 | A M Yaglom & I M Yaglom, Challenging mathematical problems with elementary solutions I, Combinatorial analysis and probability theory, Dover 1964, ISBN 0486655369 | |
| Taylor, Storozhev, Tournament of the Towns 1993-1997, AMT 1992 | A M Yaglom & I M Yaglom, Challenging mathematical problems with elementary solutions II, Problems from various branches of mathematics, Dover 1967, ISBN 0486655377 | |
| M S Klamkin, USA Mathematical Olympiads 1972-1986, MAA 1988, ISBN 0883856344 | Paul Zeitz, The art and craft of problem solving, Wiley 1999, ISBN 0471135712. (Putnam training book. Tiresomely, most of the solutions are in a separate instructors' manual, which is hard to get hold of). Comments |