A-Level Further Mathematics FULL COURSE

About Course

This comprehensive course is designed for A-Level students preparing for the Cameroon GCE and other global exams. It covers critical topics in Further Mathematics, providing in-depth knowledge and problem-solving skills. Students will explore elementary number theory, mathematical reasoning and logic, polar coordinates, linear transformations, and vector spaces. The course includes instructional videos, detailed PDF notes, quizzes, and exams to ensure thorough understanding and exam readiness.

Elementary Number Theory: Understand gcd, lcm, prime numbers, divisibility, and the Fundamental Theorem of Arithmetic.
Mathematical Reasoning and Logic: Master propositions, logical equivalences, quantifiers, proofs, and conditional statements.
Polar Coordinates: Analyze polar frames, equations, tangents, normals, and areas bounded by curves.
Linear Transformations: Explore linear transformation properties, kernel and image, inverse transformations, and eigenvalues.
Vector Spaces: Learn about vector space axioms, spans, subspaces, linear dependence/independence, and null spaces.

Course Content

ELEMENTARY NUMBER THEORY
Dive into the fundamental concepts of number theory, including gcd, lcm, prime numbers, divisibility rules, and the Fundamental Theorem of Arithmetic. Understand how to solve linear Diophantine equations and work with modular arithmetic and linear congruences.

The Greatest Common Divisor (gcd) and Least Common Multiple (lcm) of Integers

00:00
Relatively Prime Numbers and Prime Numbers

00:00
Divisibility Properties and Division Algorithm

00:00
Fundamental Theorem of Arithmetic (FTA)

00:00
Number Bases

00:00
Linear Diophantine Equations

00:00
Modular Arithmetic and Linear Congruences

00:00
Practice Problems

MATHEMATICAL REASONING AND LOGIC
Learn the principles of mathematical reasoning and logic, including propositions, truth tables, logical equivalences, quantifiers, and conditional statements. Master various proof techniques such as direct and indirect proofs, induction, and contradiction.

POLAR COORDINATES
Explore the polar coordinate system and its relationship with Cartesian coordinates. Study polar equations and curves, including Limacon, Rose, and Lemniscates. Learn how to find tangents, normals, and areas bounded by polar curves

LINEAR TRANSFORMATIONS
Understand the definition and properties of linear transformations. Analyze the kernel and image of transformations, inverse transformations, and composition of transformations. Learn about invariant points, matrix transformations, eigenvalues, and eigenvectors.

VECTOR SPACES
Study the axioms of vector spaces, spans, subspaces, and linear dependence and independence of vectors. Delve into the null space of a vector space and solve problems related to these concepts.

Student Ratings & Reviews

No Review Yet

About Course

What Will You Learn?

Course Content

ELEMENTARY NUMBER THEORY Dive into the fundamental concepts of number theory, including gcd, lcm, prime numbers, divisibility rules, and the Fundamental Theorem of Arithmetic. Understand how to solve linear Diophantine equations and work with modular arithmetic and linear congruences.

The Greatest Common Divisor (gcd) and Least Common Multiple (lcm) of Integers

Relatively Prime Numbers and Prime Numbers

Divisibility Properties and Division Algorithm

Fundamental Theorem of Arithmetic (FTA)

Number Bases

Linear Diophantine Equations

Modular Arithmetic and Linear Congruences

Practice Problems

MATHEMATICAL REASONING AND LOGIC Learn the principles of mathematical reasoning and logic, including propositions, truth tables, logical equivalences, quantifiers, and conditional statements. Master various proof techniques such as direct and indirect proofs, induction, and contradiction.

Propositions and Truth Tables

Logical Equivalence

Universal and Existential Quantifiers

Conditional Statements

Relationship Between a Theorem and Its Converse

Direct and Indirect Proof by Deduction

Proofs by Induction and Contradiction

Practice Problems

POLAR COORDINATES Explore the polar coordinate system and its relationship with Cartesian coordinates. Study polar equations and curves, including Limacon, Rose, and Lemniscates. Learn how to find tangents, normals, and areas bounded by polar curves

Polar Frame of Reference

Relationship Between Polar and Cartesian Coordinates

Polar Equations and Tracing (Limacon, Rose, Lemniscates)

Tangents and Normals to Polar Curves

Area Bounded by a Polar Curve

Practice Problems

LINEAR TRANSFORMATIONS Understand the definition and properties of linear transformations. Analyze the kernel and image of transformations, inverse transformations, and composition of transformations. Learn about invariant points, matrix transformations, eigenvalues, and eigenvectors.

Definition and Properties of Linear Transformation

Kernel and Image of a Linear Transformation

The Inverse of a Linear Transformation

Composition of Linear Transformations

Invariant Points

Image of Lines and Planes Under a Matrix Transformation

Eigenvalues and Eigenvectors

Practice Problems

VECTOR SPACES Study the axioms of vector spaces, spans, subspaces, and linear dependence and independence of vectors. Delve into the null space of a vector space and solve problems related to these concepts.

Axioms of a Vector Space

Span of a Vector

Vector Subspace

Linear Dependence/Independence of a Set of Vectors

Null Space of a Vector Space

Practice Problems

Student Ratings & Reviews

ELEMENTARY NUMBER THEORY
Dive into the fundamental concepts of number theory, including gcd, lcm, prime numbers, divisibility rules, and the Fundamental Theorem of Arithmetic. Understand how to solve linear Diophantine equations and work with modular arithmetic and linear congruences.

MATHEMATICAL REASONING AND LOGIC
Learn the principles of mathematical reasoning and logic, including propositions, truth tables, logical equivalences, quantifiers, and conditional statements. Master various proof techniques such as direct and indirect proofs, induction, and contradiction.

POLAR COORDINATES
Explore the polar coordinate system and its relationship with Cartesian coordinates. Study polar equations and curves, including Limacon, Rose, and Lemniscates. Learn how to find tangents, normals, and areas bounded by polar curves

LINEAR TRANSFORMATIONS
Understand the definition and properties of linear transformations. Analyze the kernel and image of transformations, inverse transformations, and composition of transformations. Learn about invariant points, matrix transformations, eigenvalues, and eigenvectors.

VECTOR SPACES
Study the axioms of vector spaces, spans, subspaces, and linear dependence and independence of vectors. Delve into the null space of a vector space and solve problems related to these concepts.