Please see the attached document: Curriculum PreK-3

- Order of operations
- Prime numbers, divisibility tests
- Simple fractions
- Negative numbers
- Geometrical symmetries
- Angles
- Special quadrilaterals

- Overview of prime factorization
- LCM and GCD
- Fractions with large denominators
- Algebraic laws. Distributivity (opening parentheses)
- Negative numbers. Multiplication. Absolute value
- Equations and word problems (big topic!)
- Powers of 2 and binary numbers
- Parallel lines, transversal lines, corresponding angles etc.
- Congruence tests for triangles
- Pythagorean theorem

- Basic logic (knights and knaves, logic operations)
- Set theory basics (basic operations and Venn diagrams)
- Linear equations continued. Simple inequalities (Review)
- Powers: a
^{n}a^{m}=a^{n+m}. Multiplication and division by powers of 10 (Review) - Square roots. Rational and irrational numbers
- Arithmetic and Geometric Progressions
- Probability. Basic combinatorics: permutations
- Similarity; relation with areas and volumes
- Constructions with ruler and compass
- Coordinate plane and graphs of simple functions

- Combinatorics: choosing with and without repetitions. Pascal triangle; formual for nCk (no proof, and no binomial theorem)
- Vectors and operations with them (in coordinates).
- Basic trigonometry (definition of sin, cos). Law of sines.
- Transformation of the plane. Reflections, rotations, and their compositions.
- Quadratic equation. Quadratic formula, Vieta formula. Parabola.
- Solving inequalities using interval method.
- Fibonacci numbers
- Plane patterns and symmetries.
- Overview of combinatorics. Pascal triangle and binomial formula.
- Divisibility, Euclid's algorithm, arithmetic of remainders, congruences. Application: check digits

Fundamental theorem of arithmetic - Euclidean geometry (following Kiselev). First postulates, congruence tests for triangles, alternate interior angle theorem, properties of sepcial quadrialterals, similar triangles, Thales theorem, inscribed angles.
- Elements of mathematical logic and set theory. Quantifiers. Bijection and injection. Infinite sets and cardinality.
- Functions and graphs. Even, odd, periodic, monotonic functions. Graphs of basic functions (power function, roots, sin, cos,) and their transformations. Inverse function.
- Equations of ellipse, hyperbola, parabola. Conic sections
- Exponential function. Logarithm. Equations and inequalities with exponents and logarithms.
- Polynomials; division of polynomials. Vieta formulas
- Complex numbers
- Mathematical induction
- Trigonometry. Trigonometric equations and formulas.
- Advanced geometry with vectors: Ceva theorem, Ptolemey theorem, nine point circle.
- Sets and functions. Bijections
- Infinite sets and cardinality
- Equivalence relations.Z
_{n} - Solving equivalences, invertible elements in Z
_{n}, Chinese remainder theorem - Euler function and Public Key cryptography

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