Numbers and basic operations with numbers

Number lines and examples on operations with integers

Mixed operations and the order of operations

Examples on the order of operations

Exponents and radicals

Advanced technologies for solving linear equations

Examples of solving linear equations

Set theory and solution of linear equations. Null spaces. Uniqueness. Examples of null spaces.

Quadratic equations and the Vieta theorem

Equations with radicals

Rational and irrational numbers

Operations with rational numbers

Decimals and fractions Operations with rational and irrational numbers

Introduction to mathematical reasoning

Introduction to number theory

Pythogorean triples in the number theory

Pythogorean triples and the unit circle Fermat’s theorem

Examples involving the number theory

One-variable equation

Abstract modelling for solving one dimensional equations

Examples of using mathematical reasoning and abstract modelling for solving algebraic equations

Solutions to inequalities

Graph inequalities

Advanced technologies for solving linear equations

Examples of solving linear equations

Set theory and solution of linear equations. Null spaces. Uniqueness. Examples of null spaces.

Quadratic equations and the Vieta theorem

Equations with radicals

Classification of geometric figures

Classification of angles

Geometric measures of 2-D figures

Circles

3-D figures

Exercises

Introduction to mathematical logics

Fundamental definitions of mathematical logic

Elements of model theory and algebraic logic

Elements of recursion theory

The use of math logics in algebra and geometry

Exercises

Introduction to theory of graphs

Pictographs. Examples

Frequency charts, histograms, S&L plots, B&W plots

Bar graphs

Examples: How to choose the best graph

Introduction to advanced geometry

Advanced properties of 2-D figures

Advanced properties of 3-D figures

Ceva’s theorem

Manelaus’ theorem

Introduction to theory of probability

Probability of independent and dependent events

Elements of predictions

Bar graphs

Use of the probability in banking and finance

Example: application of the prediction theory to stock market dynamics

Fundamental principles of probability and statistics

Collection, organization and representation of numerical data

Binomial Poisson distributions

Spread of a distribution, continuous distributions, properties and use of normal distribution

Bayesian’s theorem and advanced methods for prediction of random data sequances