# A Second Step to Mathematical Olympiad Problems

The International Mathematical Olympiad (IMO) is an annual international mathematics competition held for pre-collegiate students.

The material contained in this book provides an introduction to the main mathematical topics covered in the IMO, which are: Combinatorics, Geometry and Number Theory. In addition, there is a special emphasis on how to approach unseen questions in Mathematics, and model the writing of proofs. Full answers are given to all questions.

**Key Features:**

- An introduction to the main mathematical topics covered in the IMO
- Easily comprehensible to students
- Full solutions provided to all mathematical problems

**Contents:** ** Combinatorics:** A Quick Reminder; Partial Fraction; Geometric Progressions; Extending the Binomial Theorem; Recurrence Relations; Generating Functions; Of Rabbits and Postmen; Solutions;

**The Circumcircle; Incircles; Exercises; The 6-Point Circle?; The Euler Line and the Nine Point Circle; Some More Examples; Hints; Solutions; Glossary;**

*Geometry 3:***Introduction; A Problem to Solve; Mathematics: What is it?; Back to Six Circles; More on Research Methods; Georg Pólya; Asking Questions; Solutions;**

*Solving Problems:***A Problem; Euler's ϕ-function; Back to Section 4.2; Wilson; Some More Problems; Solutions;**

*Number Theory 2:***Introduction; Rules to Order the Reals By; Means Arithmetic and Geometric; More Means; More Inequalities; A Collection of Problems; Solutions;**

*Means and Inequalities:***Introduction; Inclusion–Exclusion; Derangements (Revisited); Linear Diophantine Equations Again; Non-taking Rooks; The Board of Forbidden Positions; Stirling Numbers; Some Other Numbers; Solutions;**

*Combinatorics 3:*

*Creating*

Cover: Soft

Number of Pages: 312

Author(s): **Jiagu** **Xu*** **(Former Professor of Mathematics, Fudan University, China)*

ISBN: **978-981-4327-87-9 **

- We will not be responsible for lost mails or damages for orders by normal mail option.
- No refunds or returns after purchase.
- Exchanges subject to the following:
- stock availability.
**You must contact us to raise your request within 5 working days from receipt of your order.**- Before returning or making an exchange, you are required to send us photos of the exchange products before sending out to us.
- Item to be returned must reach us within 5 working days from our email confirmation to you on the exchange arrangement.
- Item to be returned has to be in original new condition. We encourage courier or office drop-off.
- All returns are to be arranged at your own cost. We will not be responsible for damage in transit.

- Please see full terms & conditions

The International Mathematical Olympiad (IMO) is an annual international mathematics competition held for pre-collegiate students.

The material contained in this book provides an introduction to the main mathematical topics covered in the IMO, which are: Combinatorics, Geometry and Number Theory. In addition, there is a special emphasis on how to approach unseen questions in Mathematics, and model the writing of proofs. Full answers are given to all questions.

**Key Features:**

- An introduction to the main mathematical topics covered in the IMO
- Easily comprehensible to students
- Full solutions provided to all mathematical problems

**Contents:** ** Combinatorics:** A Quick Reminder; Partial Fraction; Geometric Progressions; Extending the Binomial Theorem; Recurrence Relations; Generating Functions; Of Rabbits and Postmen; Solutions;

**The Circumcircle; Incircles; Exercises; The 6-Point Circle?; The Euler Line and the Nine Point Circle; Some More Examples; Hints; Solutions; Glossary;**

*Geometry 3:***Introduction; A Problem to Solve; Mathematics: What is it?; Back to Six Circles; More on Research Methods; Georg Pólya; Asking Questions; Solutions;**

*Solving Problems:***A Problem; Euler's ϕ-function; Back to Section 4.2; Wilson; Some More Problems; Solutions;**

*Number Theory 2:***Introduction; Rules to Order the Reals By; Means Arithmetic and Geometric; More Means; More Inequalities; A Collection of Problems; Solutions;**

*Means and Inequalities:***Introduction; Inclusion–Exclusion; Derangements (Revisited); Linear Diophantine Equations Again; Non-taking Rooks; The Board of Forbidden Positions; Stirling Numbers; Some Other Numbers; Solutions;**

*Combinatorics 3:*

*Creating*

Cover: Soft

Number of Pages: 312

Author(s): **Jiagu** **Xu*** **(Former Professor of Mathematics, Fudan University, China)*

ISBN: **978-981-4327-87-9 **

- We will not be responsible for lost mails or damages for orders by normal mail option.
- No refunds or returns after purchase.
- Exchanges subject to the following:
- stock availability.
**You must contact us to raise your request within 5 working days from receipt of your order.**- Before returning or making an exchange, you are required to send us photos of the exchange products before sending out to us.
- Item to be returned must reach us within 5 working days from our email confirmation to you on the exchange arrangement.
- Item to be returned has to be in original new condition. We encourage courier or office drop-off.
- All returns are to be arranged at your own cost. We will not be responsible for damage in transit.

- Please see full terms & conditions