The Math Lab for Young Minds
Live: In-Person at ITU Lahore and Online
About Course
This course introduces fundamental concepts in logic, mathematics, and simulations using tools like GeoGebra and graph theory. Students will engage in visual learning and proof-building activities that connect mathematical reasoning with real-world applications. Each class is designed to blend theoretical concepts with interactive tools and experiments, culminating in a final project that demonstrates students’ understanding of logical and motion-based systems.
What Will You Learn?
- Understanding basic principles of motion, including horizontal and vertical movement.
- Simulating simple motion scenarios using GeoGebra to visualize speed and trajectory.
- Exploring the effects of gravity on falling objects and dispelling common misconceptions.
- Analyzing free fall motion and graphing velocity and displacement over time.
- Mastering depth-first search (DFS) and breadth-first search (BFS) algorithms for pathfinding and problem solving.
- Simulating and optimizing projectile motion, exploring how velocity affects flight time and path.
- Studying Newton’s cannonball experiment and the concept of orbital motion around a spherical Earth.
- Learning logical reasoning and proof techniques, including direct proof and proof by contradiction.
- Understanding graph theory concepts, including vertices, edges, and directed acyclic graphs (DAGs).
- Combining horizontal and vertical motion to understand projectile trajectories.
Certifications
“The Math Lab for Young Minds: Logic, Geometry and Algebra”
June’2025-July’2025
Certified Students 🌟
Here you can view and download your certificates
With lifetime access to our lecture content,
Lecture 01: Visual Proofs and Introduction to GeoGebra
- Visual Proofs
- 1+2+3+4+…+97+98+99+100
- Geometric Proof
- Algebraic Proof
- 1+2+3+4+…+97+98+99+100
- Sum of Odd numbers:
- 1+3+5+7+…
- Geometric Proof
- 1+3+5+7+…
- Introduction to geogebra
- Proof of circumference of circle (visualization of unrolling of circle’s boundary)
Lecture 02: Propsition and Quantifiers
- Revision of Gaussian’s Trick
- Proposition
- Epimende’s Paradox
- Barber’s Paradox
- Connectors and Truth Tables
- Not
- And/Conjunction
- Or/Disjunction
- XOR
- Quantifiers
- Universal Quantifiers
- Existential Quantifiers
- Theorem of division
- Properties/Theorems of even and odd numbers
- Closure Property
Help Session 01
- Visual Proofs on geogebra of :
- (a+b)^2 = a^2 + 2ab + b^2
- (a-b)^2 = a^2 – 2ab + b^2
- a^2 – b^2 = (a + b)(a – b)
- Help in solving Homework 1
Lecture 03: Direct Proofs
- Introduction to Direct Proofs
- If n is even, n^2 is even.
- Rational numbers are closed under addition.
- Proof of transitivity of divisibility
Lecture 04: Implication and Contraposition
- How they are equivalent
- Examples Proofs: If an integer’s square is an odd number then the given number is an odd number.
- Proof By Contrapositive
- Proof By Contradiction
- Proof that Primes are infinite
- Rational+Rational=Rational
- Rational+Irrational=Irrational
- √2 is an Irrational number
- De-Morgan’s Law
Lecture 05: Proof Techniques and Visual Proofs
Proof by exhaustion
- Prove that (n + 1)^3 >= 3^n if n is positive integer and n <= 4.
- Prove that n^2 >= n if n is an integer.
- If n is an integer and its square is taken then its unit digit will always be {0,1,4,5,6,9}.
- Show that there are no solutions in integers x and y of x^2+3y^2 = 8.
Constructive Proof
Prove that x, y Z such that x + y = 10.
Lecture 06: Pigeonhole Principle
Pigeonhole Principle
Cake Slice Problem
Counting
Product Rule
Sum Rule
Subtraction Rule
Division Rule
Lecture 07: Introduction to GeoGebra
Introduced the Cartesian coordinate system with x- and y-axes
Explained how to plot points using coordinate pairs (x, y)
Defined and differentiated between lines and line segments
Introduced the concept of a function as a rule assigning each input exactly one output
Practiced writing equations of functions in various forms (e.g., linear, quadratic)
Demonstrated how to graph functions and equations using tables and coordinate plotting
Discussed the concept of slope and how it indicates the steepness and direction of a line
Explained translations of graphs (shifting up, down, left, and right)
Explored how slopes and y-intercepts affect the appearance of lines on a graph
Taught how flattening (vertical compression) and shrinking (horizontal compression) change the shape of curves on the graph
Lecture 08: Graphs and Their Applications
Introduction to Graphs
Edges
Vertices
Degree
Reachability Problem
Adjacency Graph Matrix
Adjacency Graph List
Facebook in terms of Graphs
Unidirectional Graph
Twitter in terms of Graphs
Directional Graph
Dependancy Graph
Lecture 09: Linear, Quadratic, Cubic Discovery
Drawing polygons on GeoGebra
Intro to distance time graphs
Constant speed
Linear speed
Quadratic speed
Cubic speed
Motion of car w.r.t these speeds and its discovery through motion and area
Lecture 10: Discovering Sine and Cosine
- Revolving point around circle (like planets in solar system)
- Introduction to Circular System of angle measurement.
- Value of pi()
- Discovering sin and cos waves using circle
- Plotting circle using sin and cos waves
- Discovering elliptical motion using wave equations
- Making different shapes (butterfly) using sin and cos equations
Lecture 11: Freefall, Gravity and Satellite Systems
• Visualisation of acceleration due to gravity is independent of mass
• Projectile motion is the result of combination of two vectors
• How to imitate Projectile motion?
• Newton’s cannonball experiment
• How orbit works.
Lecture 12: Last Lecture
• Inverse Square Law and its importance
• Escape velocity
• Effect of velocity and height of sattelite on its orbit