Olympic Mathematics
Here is the content of the curriculum for each Olympic Mathematics course. These are the topics you will learn and master in our courses.
Pre Olympic
32 Hours: 8 Weeks, 2 weekly classes of 2 hours each.
Aimed at students with or without experience in Mathematical Olympiads, it covers a series of psychological strategies that every Olympian must follow, before, during and after taking an Olympiad test.
In addition to solving many problems, a vital part of your training is to lead a proper lifestyle that maximizes your performance. Your diet, hydration, and emotional stability greatly influence your academic performance.
This course will give you all the knowledge you need to start a proper training routine and start shining at the Olympics.
Introduction to Mathematical Reasoning
- Definitions, Axioms, Theorem, Lemma, Scholium.
- Problems vs Exercises.
- Classification of Problems
- Strategies, Tactics, and Tools.
- Research and Argumentation
- Psychological Strategies
- Creativity
- Cross Training
- Penultimate step, Desirable thought, Mental peripheral vision, other points of view.
- Methods of Argument: Direct, by Contradiction, Contrary to Truth, Basic Induction, Strong Induction.
- Fundamental Order Tactics: Geometric Symmetry, Algebraic Symmetry, Principle of the Extreme Element, Palomar Principle, Invariants.
Geometry
- Angles and Triangles.
- Congruence and Similarity of Triangles.
- Pythagoras.
Number Theory
- Divisibility Tests
- Algebraic Properties of Divisibility.
Combinatorics
- Fundamental Principle of Counting
- Permutations
- Inverted Permutations
- Combinations
- Inverted Combinations
Algebra
- Telescopic sequences and series.
- Polynomials and Higher Order Factorization.
Basic 1
48 Hours: 12 Weeks, 2 Weekly Classes of 2 Hours each.
First Olympic Training Course.
Aimed at students with experience in Mathematics Competitions.
Number Theory
- LCM, GCD and Division Algorithm.
- Fundamental Theorem of Arithmetic.
- Congruences A.
Combinatorics
- Arrays, Permutations and Combinatorics.
- Double Counting
- Bijections
Geometry
- Congruence and Parallelism
- Areas and Proportions
- Pythagoras Theorem
Algebra:
- Higher-order factorization
- Mathematical logic
- Set theory
Basic 2
48 Hours: 12 Weeks, 2 Weekly Classes of 2 Hours each.
Second Olympic Training Course.
Aimed at students with experience in Mathematics Competitions.
Number Theory
- Bases.
- Congruence B (Fermat’s Theorem, Wilson’s Theorem, Euler’s Theorem)
- Order and primitive roots.
Combinatorics
- Binomial and Multinomial Theorem.
- Inclusion and Exclusion Principle.
- Partitions
Geometry
- Geometry of the Triangle A
- Geometry of the Triangle B
- Geometry of the Circle A
Algebra:
- PPolynomials A
- Functions
- Progressions and Summation
Intermediate 1
48 Hours: 12 Weeks, 2 Weekly Classes of 2 Hours each.
Third Olympic Training Course.
Aimed at students with experience in Mathematics Competitions.
Number Theory
- Lifting the Exponent.
- Pythagorean Triplets.
- Congruence C (Linear Equations modulo m CRT).
Combinatorics
- Combinatorial Configurations and the Casillas Principle
- Probabilities
- Game Theory
Geometry
- Geometry of the Circle B
- Geometric Locus
- Homothecy and Similarity
Algebra:
- Complex Numbers
- Inequalities A
- Polynomials B
Intermediate 2
48 Hours: 12 Weeks, 2 Weekly Classes of 2 Hours each.
Fourth Olympic Training Course.
Aimed at students with experience in Mathematics Competitions.
Number Theory
- Law of Quadratic Reciprocity.
- Quadratic Diophantine equations and sum of squares A.
- Quadratic Residues and Legendre Symbol.
Combinatorics
- Burnside’s Lemma
- The Extreme Element Principle
- Invariants and Monovariants
Geometry
- Analytical Geometry A (Vectors)
- Analytical Geometry B (Trigonometry)
- Baricentric Coordinates A
Algebra:
- Functional Equations A
- Polynomials C
- Inequalities B
Advanced 1
48 Hours: 12 Weeks, 2 Weekly Classes of 2 Hours each.
Fifth Olympic Training Course.
Aimed at students with some experience in Mathematics Competitions.
Number Theory
- Quadratic Diophantine equations and sum of squares B.
- Fermat’s infinite descent.
- Zsigmondy.
Combinatorics
- Graph Theory A
- Graph Theory B
- Generating Functions A
Geometry
- Barycentric Coordinates B
- Complex Numbers in Geometry
- Inversion A
Algebra:
- Sequences and Series
- Geometric Inequalities
- Recurrent Sequences
Avanzado 2
48 Hours: 12 Weeks, 2 Weekly Classes of 2 Hours each.
Sixth Olympic Training Course.
Aimed at students with some experience in Mathematics Competitions.
Number Theory
- Pell’s equations.
- Multiplicative functions A.
- Multiplicative functions B.
Combinatorics
- Generating Functions B
- Ramsey Theory
- Combinatorial Geometry
Geometry
- Inversion B
- Projective Geometry A
- Projective Geometry B
Algebra:
- Maximum and minimum of derivable functions
- Inequalities C
- Functional Equations B
You can also learn these topics separately in our private classes.
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