Build an Unshakeable Math Foundation—Without the Memorization

Struggling to make math click? You aren't bad at math—you've simply been taught to memorize formulas instead of understanding the principles behind them.

This course bridges the gap between frustration and mastery. Covering Precalculus, Calculus 1, Discrete Math, and Electrical Engineering Ohm's Law within one unified, concept-first framework, you'll transform abstract equations into clear, intuitive concepts you can confidently apply.

How This Course Is Designed

Throughout the course, every topic is taught through:

Concept-first teaching that builds genuine understanding.
Step-by-step worked examples with detailed explanations.
Visual demonstrations that make abstract ideas intuitive.
Carefully designed quizzes that reinforce long-term learning.
A logical progression that gradually develops confidence without unnecessary shortcuts.

Whether you're preparing for school, university, engineering, or simply want to truly understand mathematics, this course provides a structured learning path that builds lasting confidence from the ground up.

What You'll Learn:

Precalculus

Understand and recognize functions using the vertical line test.
Find the domain and range of any given function with absolute accuracy.
Solve average rate of change problems step-by-step with zero guesswork.
Analyze function behaviors to instantly categorize even, odd, or composite functions.
Determine inverse functions and map the domain and range of their inverse structures.
Locate global and local extrema using precise graphic properties.

Trigonometry

Apply triangle properties and use pythagoras theorem to solve right triangles.
Evaluate all six trigonometric functions (sine, cosine, tangent, cosecant, secant, and cotangent).
Master trigonometric functions of standard angles.
Apply key identities, including complementary angle, pythagorean, negative angle, sum/difference, and product-to-sum formulas.
Evaluate non-standard angles cleanly using core trigonometric identities.
Utilize the laws of sines and cosines to solve for unknown sides and angles of any triangle.
Prove triangle similarity and use similar triangle properties to calculate unknown dimensions.

Calculus 1

Define and evaluate limits of a function directly using graphical analysis.
Calculate one-sided limits (left-hand and right-hand limits) to assess function's local behavior around a given point on graph.
Assess function continuity and track structural asymptotes from its given graph.
Define and understand derivatives of a function.
Execute the first principle of calculus to find derivative of a function from scratch.
Master all fundamental derivative rules: power, constant, sum, difference, product, quotient, and the vital chain rule.
Solve trigonometric derivatives using a structured sequence of step-by-step mathematical examples.
Master exponential and logarithmic derivatives with absolute theoretical precision

Discrete Math: Set Theory

Master Set Basics: Master set definition and understanding.
Master Set Representation: Master representing sets in different forms.
Master Set Cardinality: Master figuring set cardinality |S| of any given set.
Master all Types of Sets: Master finite set, infinite set, empty set (Ø), singleton set, equal sets (A = B), equivalent sets (A ~ B), disjoint sets, and overlapping sets.
Master Subset & Superset: Explore subset (A ⊆ B), proper subset (A ⊂ B), and superset (A ⊇ B)
Master Special Sets: Understand power set (P (A)) and universal set (U)
Master all Set Operations: Master union (A ∪ B), intersection (A ∩ B ), set difference (A-B) , and complement (A')
Master Cartesian Products: Master cartesian/cross products (A × B) of sets step-by-step.
Master Visual Problem Solving using Venn Diagram: Master representing sets and set operations on venn diagram, and solving complex problems visually using venn diagrams.

Discrete Math: Relations

Master Relation Basics: Master relations and their representation.
Master Domain and Range of a Relation: Master finding the exact domain and range of a relation.
Master all Types of Relations: Master empty, universal, identity, and inverse relation.
Master all Properties of Relations: Master reflexive, symmetric, transitive, and equivalence relation.

Discrete Math: Functions

Master Function Basics: Master functions and determining whether a given relation qualifies as a function.
Master Domain, Codomain, and Range of a Function: Master finding exact domain, codomain, and range of a function.
Master all Types of Functions: Master injective (one-to-one), surjective (onto), and bijective (one-to-one correspondence) function.
Master Even and Odd Function: Master even and odd function, and determining if a given function is even, odd or neither.
Master Composite Function: Master function composition and evaluating function composition.
Master Inverse Function: Master inverse function and finding the inverse function

Discrete Math: Mathematical Induction

Master the Principle of Mathematical Induction: Master the core principle of mathematical induction, step-by-step.
Master Proving Sum of Squares: Master proving the sum of squares of the first n natural numbers using inductive logic.
Master Proving Progressions: Master proving the sum of Arithmetic Progression (AP) and Geometric Progression (GP).
Master Proving a Result from Geometry: Master applying mathematical induction in proving a geometric result.
Master Proving Inequality and Divisibility: Learn applying induction in proving algebraic inequality and divisibility.
Master Solving a Brain-Teaser: Master solving a brain-teasing real world problem using mathematical induction.
Master Solving the Towers of Hanoi Puzzle: Master applying induction to the iconic Towers of Hanoi puzzle.
Master Computer Science Program Correctness Proof: Master applying induction in computer science for program correctness proof.

Fundamentals of Electrical Ohm's Law

Understand Current and its Relationship with the Voltage (the Current-Voltage Relationship) with the help of Visualization;
Understand the Current-Resistance Relationship with the help of Visualization;
Understand the Ohm's Law - the basic definition of Ohm's Law and its understanding;
Solve basic circuit problems on Ohm's Law;
Do Word problems on Ohm's Law; and
Understand the V-I graph (voltage-current graph) - Understand the V-I graph, the slope of the V-I graph and do practice problems based on V-I graphs.

Who Should Enroll in This Course:

Mathematics Students who want to build a strong foundation in Precalculus, Trigonometry, Calculus 1, and Discrete Mathematics through concept-first learning.
University Students looking to strengthen their mathematical foundation for higher studies.
Engineering Students looking to strengthen the mathematical foundation required throughout their engineering education.
Electrical Engineering Students who want to build a strong foundation in mathematics while mastering the fundamental concept of Ohm's Law.
Physics Students looking to strengthen the mathematical and electrical foundations needed for advanced physics.
Computer Science Students seeking a solid foundation in Calculus 1, Discrete Mathematics and mathematical reasoning.
School Students preparing for high-school mathematics and university-level coursework.
Adult Learners returning to mathematics after a break and looking for a structured, step-by-step learning experience.
Self-Learners who want to replace memorization with genuine understanding and build lasting confidence in mathematics.
Anyone Interested in Learning Mathematics Properly through intuitive explanations, rigorous reasoning, worked examples, visualizations, and quizzes.

Stop memorizing mathematics. Start understanding it. Build an unshakeable foundation in mathematics while simultaneously developing the problem-solving skills that will continue benefiting you for years to come. Enroll today.