Fundamental Concepts in Mathematics

Arithmetic
- Basic operations: addition, subtraction, multiplication, division.
- Order of operations: PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction).
Algebra
- Variables and constants.
- Expressions and equations: solving for x.
- Functions: linear, quadratic, exponential.
Geometry
- Shapes and properties: triangles, circles, squares, polygons.
- Theorems: Pythagorean theorem, properties of angles.
- Perimeter, area, and volume calculations.
Trigonometry
- Sine, cosine, and tangent functions.
- Right triangles and the unit circle.
- Trigonometric identities and equations.
Calculus
- Limits: understanding continuity and behavior of functions.
- Derivatives: rates of change and slopes of curves.
- Integrals: area under curves and accumulation of quantities.
Statistics
- Data collection and analysis: mean, median, mode.
- Probability: basic principles and calculations.
- Distributions: normal distribution, binomial distribution.
Linear Algebra
- Vectors and matrices.
- Systems of equations.
- Eigenvalues and eigenvectors.
Number Theory
- Prime numbers and factors.
- Divisibility rules.
- Modular arithmetic.

Theorems and Proofs: Establishing truths based on axioms and previously proven concepts.
Mathematical Modeling: Using mathematical methods to represent real-world phenomena.
Problem-Solving Strategies: Breaking down problems, using diagrams, and testing solutions.

Graphing Calculators: For complex calculations and visualizing functions.
Computer Software: MATLAB, Python, R for statistical analysis and simulations.
Online Resources: Khan Academy, Coursera for tutorials and practice problems.

Arithmetic: Involves basic operations including addition, subtraction, multiplication, and division; follows the order of operations acronym PEMDAS.
Algebra: Utilizes variables and constants to create expressions and equations, focusing on solving for unknowns (x) and includes various functions like linear, quadratic, and exponential.
Geometry: Studies shapes such as triangles, circles, squares, and polygons; includes key theorems like the Pythagorean theorem and essential calculations for perimeter, area, and volume.
Trigonometry: Centers around sine, cosine, and tangent functions, particularly in right triangles and the unit circle; incorporates important trigonometric identities and equations.
Calculus: Deals with limits to understand the continuity of functions; focuses on derivatives for assessing rates of change and slopes, and integrals for calculating area under curves and aggregating quantities.
Statistics: Encompasses data collection and analysis methods, highlighting measures like mean, median, and mode; integrates probability concepts along with distributions like normal and binomial distributions.
Linear Algebra: Focuses on vectors and matrices, crucial for solving systems of equations, and explores concepts of eigenvalues and eigenvectors.
Number Theory: Investigates properties of prime numbers and factors, includes divisibility rules, and covers modular arithmetic principles.

Theorems and Proofs: Develop truths based on established axioms and previous proofs, forming the foundation of mathematical understanding.
Mathematical Modeling: Applies mathematical methods to illustrate and solve real-world phenomena effectively.
Problem-Solving Strategies: Emphasizes techniques for breaking down complex problems, utilizing diagrams, and testing different solutions for effectiveness.

Finance: Involves calculations related to interest rates, budgeting strategies, and financial modeling techniques to inform economic decisions.
Engineering: Utilizes mathematical concepts for structural analysis and optimization challenges, ensuring efficiency and safety in design.
Science: Relies on statistical analysis and experimental design to draw conclusions from data and support scientific inquiries.

Graphing Calculators: Essential for executing complex calculations and visualizing mathematical functions in an intuitive manner.
Computer Software: Tools like MATLAB, Python, and R are pivotal for advanced statistical analysis and simulations.
Online Resources: Educational platforms such as Khan Academy and Coursera provide tutorials and practice problems to enhance learning and understanding.