A structured record of my self-study in mathematics, including study logs, problem walkthroughs, deeper explorations and reflections, and preparation for advanced coursework.
Professor Leonard – Calculus 3 – 13.1: Introduction to Multivariable Functions (Domain, Sketching, Level Curves) Thomas – 14.1 Functions of Several Variables Multivariable FunctionsUp to this point, calculus operations have involved a single variable. A function relates one or more…
Professor Leonard – Calculus 3 – 12.4: Velocity & Acceleration of Vector Functions Thomas – 13.5 Tangential & Normal Components of Acceleration; 13.6 Velocity & Acceleration in Polar Coordinates We’ve seen velocity and acceleration before, so the concept is essentially a…
Professor Leonard – Calculus 3 – 12.3: TNB (Frenet-Serret) Frames, Curvature, Torsion, Encapsulation Thomas – 13.4 Curvature and Normal Vectors of a Curve; 13.5 Tangential and Normal Components of Acceleration TNB FramesTNB Frames, also known as Frenet-Serret frames, describe how…
I’ve been learning Linear Algebra for five months now. I effectively started at the very beginning of 2026, and have chewed on a piece of it nearly every day since. I’ve watched Gilbert Strang’s lectures, done the reading in his…
Hermitian & Unitary MatricesMIT OCW 18.06SC Sections – Lectures & Reading:Lecture 26: Complex Matrices; Fast Fourier Transform (FFT)Strang 9.2 – Hermitian and Unitary Matrices Complex Transpose and Conjugate Transposing matrices is foundational in Linear Algebra, as it lets us move…
MIT OCW 18.06SC Sections – Lectures & Reading:OCW Lecture 25: Symmetric Matrices & Positive DefinitenesssStrang 6.4 & 6.5 Symmetric Matrices What is a Symmetric Matrix?A matrix is symmetric if it is equal to its transpose. In Linear Algebra talk, we…
Professor Leonard – Calculus 312.3: Arc Length/Parameterization, TNB (Frenet-Serret) IntroThomas – 13.3 ‘Arc Lengths in Space’ Arc Length By now we’re familiar with parametric equations. They’re those very useful equations that describe a curve by expressing each coordinate as a…
MIT OCW 18.06SC Sections – Lectures & Reading: Lecture 24: Markov Matrices; Fourier Series Strang 10.3 & 10.5 Matrices as Models of Change Matrices can describe how systems change through iterations or steps. With a matrix’s rules defined, we can…
MIT OCW 18.06SC Sections – Lectures & Reading: Lecture 22: Diagonalization & Powers of A Strang 6.2 Diagonalizing a matrix is rewriting it in a form such as Where D equals a diagonal matrix of eigenvalues and P contains the…
MIT OCW 18.06SC Sections – Lectures & Reading: Lecture 21: Eigenvalues and Eigenvectors Strang 6.1 Early on in Linear Algebra I tried my best to see the study of Linear Algebra as the study of linear transformations, as functions that…
