COURSE UNIT TITLE

: ADVANCED MATHEMATICAL PROBLEM SOLVING TECHNIQUES FOR OLYMPIADS

Description of Individual Course Units

Course Unit Code Course Unit Title Type Of Course D U L ECTS
MAT 4069 ADVANCED MATHEMATICAL PROBLEM SOLVING TECHNIQUES FOR OLYMPIADS ELECTIVE 4 0 0 7

Offered By

Mathematics

Level of Course Unit

First Cycle Programmes (Bachelor's Degree)

Course Coordinator

ASSISTANT PROFESSOR CELAL CEM SARIOĞLU

Offered to

Mathematics

Course Objective

This course aims to introduce students to advanced problem techniques for the problems in mathematical olympiads.

Learning Outcomes of the Course Unit

1   will be able to use important identities and inequalities to solve olympiad problems
2   will be able to use calculus and analysis techniques to solve olympiad problems
3   will be able to use geometric and trigonometric tools to solve olympiad problems
4   will be able to use linear algebra tools to solve olympiad problems
5   will be able to use number theoretic methods to solve olympiad problems
6   will be able to use combinatorial techniques to solve olympiad problems

Mode of Delivery

Face -to- Face

Prerequisites and Co-requisites

None

Recomended Optional Programme Components

None

Course Contents

Week Subject Description
1 Methods of Proof
2 Identities and Inequalities
3 Polynomials and olympiad problems
4 Linear algebra for olympiad problems
5 Abstract algebra for olympiad problems
6 Sequences and Series
7 Calculus techniques for olympiad problems
8 Equations with functions as unknowns
9 Geometry in olympiad problems
10 Trigonomety in olympiad problems
11 Integer Valued Sequences and Functions, Arithmetic
12 Arithmetic, Diophantine Equations
13 Combinatorial and Probability techniques for olympiad problems
14 Graph theory for olympiad problems

Recomended or Required Reading

Textbooks:
1. Gelca, R. and Andreescu, T., Putnam and Beyond, Springer, 2007
2. Andreescu, T. and Enescu, B., Mathematical Olympiad Treasures, Birkhauser, 2011
Supplementary Books:
3. Andreescu, T. and Gelca, R., Mathematical Olympiad Challenges, 2nd edition, Birkhauser, 2008
4. Andreescu, T., Mortici, C. and Tetiva, M., Mathematical Bridges, Birkhauser, 2017
5. Djukic, D., Jankovic, V., Matic, I. and Petrovic, N., The IMO Compendium: A Collection of Problems Suggested for The International Mathematical Olympiads: 1959-2009, 2nd Edition, Springer, 2011
6. Shklarsky, D. O., Chentzov, N. N. and Yaglom, I.M., The USSR Olympiad Problem Book: Selected Problems and Theorems of Elementary Mathematics, 3rd edition, Dover, 2013
7. Cvetkovski, Z., Inequalities: Theorems, Techniques and Selected Problems, Springer, 2012
8. Small, C. G., Functional Equations and How to Solve Them, Springer, 2007
9. Grigorieva, E., Methods of Solving Sequence and Series Problems, Birkhauser, 2016
10. Grigorieva, E., Methods of Solving Number Theory Problems, Birkhauser, 2018
11. Grigorieva, E., Methods of Solving Nonstandart Problems, Birkhauser, 2015
12. Grigorieva, E., Methods of Solving Complex Geometry Problems, Birkhauser, 2015
13. Posamentier, A. S. and Salkind, C. T., Challenging Problems in Geometry, Dover, 2012
14. Posamentier, A. S. and Salkind, C. T., Challenging Problems in Algebra, Dover, 2012
15. Prilepko, A.I., Problem Book in High-School Mathematics, Mir, 1985

Planned Learning Activities and Teaching Methods

Lecture notes, presentation, problem solving, discussion.

Assessment Methods

SORTING NUMBER SHORT CODE LONG CODE FORMULA
1 MTE MIDTERM EXAM
2 QUZ QUIZ
3 ASG ASSIGNMENT
4 FIN FINAL EXAM
5 FCGR FINAL COURSE GRADE (RESIT) MTE * 0.30 + QUZ * 0.10 + ASG * 0.10 + FIN * 0.50
6 RST RESIT
7 FCGR FINAL COURSE GRADE (RESIT) MTE * 0.30 + QUZ * 0.10 + ASG * 0.10 + RST * 0.50


Further Notes About Assessment Methods

None

Assessment Criteria

30% (Midterm examination) +10%(Quiz)+%10(Homework assignment)+50% (Final examination)

Language of Instruction

English

Course Policies and Rules

The student is responsible for attending 70% of the courses throughout the semester. Action will be taken within the framework of the relevant regulations regarding unethical behavior that may occur in classes and exams. You can obtain the DEU Faculty of Science teaching and exam practice principles regulation from http://web.deu.edu.tr/fen.

Contact Details for the Lecturer(s)

Asst. Prof. Dr. Celal Cem SARIOĞLU
E-mail: celalcem.sarioglu@deu.edu.tr
Phone: +90 232 301 8585
Office: B212 (Mathematics Department)

Office Hours

To be announced later.

Work Placement(s)

None

Workload Calculation

Activities Number Time (hours) Total Work Load (hours)
Lectures 14 4 56
Preparations before/after weekly lectures 13 2 26
Preparation for midterm exam 1 15 15
Preparation for final exam 1 20 20
Preparation for quiz etc. 2 7 14
Preparing assignments 2 7 14
Preparations before/after weekly lectures 13 2 26
Final 1 2 2
Midterm 1 2 2
Quiz etc. 2 1 2
TOTAL WORKLOAD (hours) 177

Contribution of Learning Outcomes to Programme Outcomes

PO/LOPO.1PO.2PO.3PO.4PO.5PO.6PO.7PO.8PO.9PO.10PO.11PO.12PO.13
LO.1555435453344
LO.2555435453344
LO.3555435453344
LO.4555435453344
LO.5555435453344
LO.6555435453344