Engineering & Science, Abridged (2026 AD) · library · engsci-abridged
Concise mathematical, scientific, and engineering notes written during the University of Toronto EngSci program and the Caltech CNS PhD, published as course-era facsimiles. These are personal notes, not official University of Toronto or Caltech course materials.
These are immutable course-era notes written for rapid review and future reference. They may contain errors, omissions, old notation, or course-specific conventions. New EngSci++ editions are independently reviewed and versioned; they do not silently replace these facsimiles.
Aman Bhargava
Caltech information theory after Cover and Thomas ch. 1–10: entropy, AEP, source and channel coding, with proof sketches of the main results.
Contains three incomplete legacy Todo sections, preserved as written.
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sha256 9eb7a00b35a3217f1d4a0d24e3c37932f832f3a3a467b3c39920be1478be1233source revision ce2570c8f07aAman Bhargava
Parameter estimation (ML, MAP, LMS), hypothesis testing, naive Bayes, LDA/QDA, and graphical-model inference.
sha256 8a5bae4eed1075f3f40e3e17cd1037b24ef15e658c4d4a8915404fdc2d44c46asource revision ce2570c8f07aAman Bhargava
Continuous- and discrete-time LTI systems, LCCDEs, and Fourier representations for signal analysis and communications.
sha256 b01e6880f06cd4905039749d73eb3f217e09afec2af1a64932f939e00bf89caesource revision ce2570c8f07aAman Bhargava
Asymptotics, graphs and graph search, minimum spanning trees, shortest paths, and algorithm-design foundations.
sha256 3790b681938abfd8eeadabe5ba8acfb8de495f08412de5aaf8be11268163ad75source revision ce2570c8f07aAman Bhargava
Vector spaces, projections, linear maps, eigendecompositions, and the matrix algebra behind optimization.
sha256 6d459bea6d38bc7c710268079f3edeeb4af9c0e90422727c559bda2aeb3a52fasource revision ce2570c8f07aEli Scott and Aman Bhargava
A compact materials-science need-to-know summary, co-written with Eli Scott.
sha256 67b690328e27536e49ef711e14e055586447eb12eeb98cf0e3d2a751fc4ebcacsource revision ce2570c8f07aAman Bhargava
Electrostatics and magnetostatics: Coulomb and Gauss laws, potentials, dielectrics, capacitance, and field energy.
sha256 59887fc6b42a70f579a7c8d5e470b2f41636a89ba08348e13a502b075e473141source revision ce2570c8f07aAman Bhargava
Axiomatic probability, conditioning and Bayes, random variables, expectation, and core statistical inference.
sha256 1e7dc0b1dc8a595d8051d821fda4b926ee689084f4b9b80edf44b8e0ec46f96csource revision ce2570c8f07aAman Bhargava
Schroedinger's equation, matter waves, particle in a box, and the bridge from quantum to thermal physics.
sha256 98df86bbab83b805d45c8b5e56bfcc09b276c1f46e51e92e9c977eaf5917a394source revision ce2570c8f07aAman Bhargava
The back half of vector calculus (after MAT195) plus introductory fluid dynamics with a focus on statics.
sha256 27f78b4ae315327f6c96cd4ace98f2367815d944f1193343380eebd4b98b2198source revision ce2570c8f07aAman Bhargava
Part 2 of the EngSci thermodynamics and heat transfer sequence, in abridged reference form.
sha256 08730761087a0d5010a90a3af4b478aab0ca5d5fd373fa909bf6d0c7ea1a78bcsource revision ce2570c8f07aAman Bhargava
First-order ODE methods, integrating factors, exact equations, and eigen-analysis of first-order systems.
sha256 902926418a2a53c31377e32528c58c571edb6d4c7e3fe76d368db2cd356c9db1source revision ce2570c8f07aAman Bhargava
Oscillators (simple, damped, forced, coupled), standing and travelling waves, and dispersion.
sha256 cb490869948e15112eaf0f379c3ca2779c29266aa508a20838756d35b756f799source revision ce2570c8f07aAman Bhargava
Textbook-following notes from first-year EngSci calculus.
sha256 b1f9646f6652eb1281f5789a9b3c0c21f25e1953c5e36f52120ea0fc6dc4cd43source revision ce2570c8f07aAman Bhargava
Lecture notes from introductory materials science.
sha256 3f0f0ac6e6ebcddd001eba28e84c9316fb2a045437aeaadc69ac4f5297fa66casource revision ce2570c8f07aAman Bhargava
Notes from first-year EngSci computing.
Released 2026-07-27 on Aman's confirmation that the embedded diagrams are his own.
sha256 60fb8a04ad7299882e756953659538b7ac8b3d5fa5145e9dcf9caec3d559f044source revision ce2570c8f07aAman Bhargava
Boolean algebra, digital logic and memory circuits, microprocessor concepts, and assembly programming.
Released 2026-07-27 on Aman's confirmation that the embedded diagrams are his own.
sha256 13f599c132e2e748d86ee04e1e8bd95274a46c19ffdee2bb8b3b9a12cd9b1b71source revision ce2570c8f07aAman Bhargava
Handwritten midterm summary: state-variable and LTI formulations, the residue method, transfer functions, time response by poles, and matrix-exponential solutions.
Handwritten facsimile with no machine-readable text; the description above is the accessible summary.
sha256 44d8e2db16fec6a96ee4c2ae578d05ddf2e0b4de7affee7094559fd5a54543dasource revision ce2570c8f07aAman Bhargava
Handwritten summary: feedback control and principle-of-the-argument (Nyquist) analysis.
Handwritten facsimile with no machine-readable text; the description above is the accessible summary.
sha256 a2bcde012d7a4f32632b5dbcc66e6a3411a2be55cd011e4434093f39a65d0857source revision ce2570c8f07aNew reviewed works (currently the Scientific Machine Learning working edition) live at /library/engsci-plus-plus/. This page holds only immutable legacy facsimiles and disclosed historical memos.
Aman Bhargava and Claude-3 Opus
An exploratory memo proposing an equivalence between abstraction and long-time-horizon prediction.
Historical draft with unresolved citation placeholders; not a reviewed EngSci++ result.
sha256 04329f8f298c233c079c5194ea8208048b3a45d899322bc4fba71536c139ab15source revision ce2570c8f07aAman Bhargava
An analysis of latent representations in optimal Bayesian filters trained for multi-class classification under noise.
Historical theory draft, archived as-is; not the peer-reviewed edition of this line of work.
sha256 6f8762949cc24f3ae74fe014e4c1a927a80bba06816bd8b64669a7d96ba45f37source revision ce2570c8f07aAman Bhargava
A theory memo arguing that Bayesian-optimal multi-classification implies abstract internal representations.
Historical theory draft, archived as-is; not the peer-reviewed edition of this line of work.
sha256 c318e4367b3b4f1a1a0e5a89dc3902692a2ab5e87fcd1426c8aa82abe05a049fsource revision ce2570c8f07aAman Bhargava
The UltraReps variant of the input-space representation analysis.
Historical theory draft, archived as-is; not the peer-reviewed edition of this line of work.
sha256 7159cb43d409822b24a3ca08b0de2f5c5b577f669c5fbc7459ca30f60fb81edesource revision ce2570c8f07a