Introduction to Vectors and Matrices

A comprehensive prep sequence for the most challenging questions on the ACT Math and Science sections. It focuses on high-level conceptual blueprints for math topics like complex numbers and matrices, alongside speed-reading and data-interpretation strategies for the Science section.

A comprehensive ACT Math preparation program focusing on essential strategies, high-yield Algebra and Geometry concepts, and realistic practice to boost scores.

This mathematical physics sequence explores the coordinate systems necessary for solving problems involving complex shapes, moving beyond Cartesian coordinates to General Curvilinear systems. Students derive scale factors, volume elements, and differential operators, culminating in solving Laplace's equation and understanding metric tensors.

A comprehensive exploration of linear recurrence relations, from first-order foundations to complex second-order systems and real-world predator-prey modeling. Undergraduate students transition from recursive thinking to closed-form solutions, applying discrete math to algorithm analysis and biology.

A graduate-level exploration of discrete dynamical systems, moving from linear growth models to the complex, chaotic behavior of the logistic map. Students apply recursive sequences to model biological and economic phenomena, emphasizing stability analysis and bifurcation theory.

An advanced exploration of vector-valued functions and their applications in modeling 2D motion and force, preparing students for multivariable calculus.

A comprehensive unit on parametric equations and their applications in modeling motion. Students move from the basics of parametric curves to advanced calculus concepts like derivatives, concavity, vectors, and arc length.

A graduate-level exploration of expected value applications in finance, covering utility theory, portfolio optimization, risk-neutral pricing, and tail risk metrics. Students transition from theoretical foundations to computational implementation using Monte Carlo methods.

This advanced sequence explores systems of linear equations through the lens of computational linear algebra. Graduate students will move from theoretical existence and uniqueness in vector spaces to matrix factorizations, algorithmic complexity, numerical stability, and iterative methods for large-scale systems.

This sequence explores the geometric interpretation of matrices, treating them as operators that transform space. Students move from calculation to visual application, using matrices to represent coordinates, perform translations/dilations, and apply rotations/reflections via matrix multiplication.

A comprehensive sequence on matrix operations, focusing on determinants, inverses, and their application in solving linear systems and cryptography. Students move from basic calculations to advanced problem-solving techniques.

A comprehensive unit for 10th-grade students exploring matrix operations, from basic dimensions and notation to complex multiplication and real-world applications in inventory management.

Students transition from algebraic addition and subtraction of complex numbers to a visual, vector-based representation on the complex plane. This lesson uses a provided video as a foundation for algebraic mastery before extending into graphical verification.

Students will solve systems of linear equations derived from the geometric properties of mutually tangent circles, connecting spatial relationships to algebraic solutions.

Students explore the geometric representation of complex numbers, connecting the modulus formula to the Pythagorean theorem and distance formula through visualization and practice.

An undergraduate-level introduction to visualizing vectors as multi-dimensional data containers. Students explore real-world applications from catering costs to nutritional data, shifting the perspective of vectors from geometric arrows to abstract data structures.

A high school mathematics lesson focused on applying vector addition and bearing calculations to real-world navigation scenarios, specifically airplanes and watercraft.

An introductory lesson on vectors in the coordinate plane. Students distinguish between scalars and vectors, learn component form notation, and practice plotting vectors through a collaborative 'Battleship' style activity.

A lesson for Advanced Precalculus students focusing on expressing vectors as linear combinations of the unit vectors i and j, featuring physics-based force problems and rapid-fire conversion practice.

A high-school geometry or pre-calculus lesson focusing on converting vectors from magnitude and direction to component form through a hands-on 'robot programming' simulation. Students use trigonometry to translate movement commands into x and y displacements.

Students will explore the geometric representation of complex numbers and discover how complex addition corresponds to vector addition and the parallelogram rule.

A Pre-Calculus lesson on solving 3x3 systems of equations to find quadratic models, featuring a manual elimination method and a matrix inverse method using graphing calculators.

A Pre-Calculus lesson connecting algebraic complex number addition to geometric vector addition on the complex plane using a 'Vector Walk' approach. Students visualize addition as head-to-tail movements on a grid.

This lesson introduces the Rule of Sarrus as a shortcut for finding 3x3 determinants, comparing its efficiency against the standard cofactor expansion method through a competitive 'Method Battle'.