Description of Advanced Mathematics Programs and Curriculum

Lebanon: Description of the Advanced Mathematics Programs and Curriculum

At Grade 12, students receive a solid mathematical foundation with the aim of preparing them to pursue their studies as teachers, engineers, and researchers. The mathematics competencies students must have in each domain are provided in the table below.

Domain Competencies
Mathematical Reasoning Recognize the difference between a mathematical explanation and concrete or experimental evidence

Make conjectures and discover means to test them

Carry out proofs using various modes of reasoning

Analyze and prove a statement of necessary and sufficient conditions

Recognize a universal statement, a statement of existence, and a statement of uniqueness

Evaluate a mathematical argument and criticize a proof

Carry out an inductive proof

Problem Solving Formulate a problem out of situations studied in mathematics, in other sciences, or encountered in real life

Use various mathematical interpretations to represent the information given in a problem, figure out a convenient strategy to solve it, and take various approaches to make this strategy work using mathematical knowledge

Discuss the validity of obtained solutions

Communication Give a summary of a mathematical document

Take notes on a mathematical lecture

Critique a mathematical presentation

Write a proof correctly

Spatial Prove and apply the properties of solid figures and conics

Characterize plane or space figures using vector notation

Study geometric problems analytically

Determine the effect of transformations on plane figures

Numbers and Algebra Analyze the extensions of the sets of numbers (natural numbers, integers, rational numbers, real numbers, complex numbers)

Study the properties of complex numbers and their use in geometry and trigonometry

Generalize fundamental mathematical notions (set, relation, binary operation, and propositional calculus)

Acquire an example of structure

Develop mathematical tools for numerical calculations, and for solutions of systems of equations and inequalities

Calculus Acquire the fundamental concepts of limit, continuity, and differentiability, and use them graphically

Analyze the graphs of polynomial, rational, irrational, trigonometric, logarithmic, and exponential functions

Integrate functions and solve simple differential equations

Statistics and Probability Organize information and represent it graphically

Study the characteristics of a statistical distribution of one variable

Solve simple probability problems, mainly in discrete cases where the events are equally likely