Deep Notes — Math, Physics, Bio, CS, Stats

Advanced Math highlights

integrals, series, taylor expansions, multivariable calculus, linear algebra (svd, eigen), ODE/PDE basics, real analysis intuition. focus on geometric meaning of linear algebra and practice changing coordinates for integrals.

Physics & Thermo

lagrangian mechanics, maxwell's equations in words, entropy and free energy, statistical ensembles and Boltzmann distribution — conceptual ties between microscopic behavior and macroscopic laws.

Chemistry & Organic patterns

kinetics vs thermodynamics, mechanism patterns (nucleophile/electrophile), spectroscopy ideas. conceptual only. lab work requires supervision.

Biology & Molecular

central dogma, gene regulation basics, cell signaling, population genetics overview. modern tools described conceptually only.

Computer Science & ML

algorithms, data structures, complexity, database fundamentals, ML taxonomy, neural net intuition, regularization and evaluation methods.

Statistics & Inference

distributions, CLT, confidence intervals, hypothesis testing concepts, Bayesian update intuition and when to prefer it.

Worked Examples & Step-by-step Solutions

Math: Evaluate ∫_{0}^{1} x * e^{x^2} dx

Solution idea: use substitution u = x^2, du = 2x dx so x dx = du/2

Let u = x^2 → du = 2x dx → x dx = du/2
When x = 0 → u = 0; x=1 → u=1
Integral becomes (1/2) ∫_{0}^{1} e^{u} du
(1/2)(e^{u}) |_{0}^{1} = (1/2)(e - 1)

Answer: (e - 1)/2

Linear Algebra: Find eigenvalues of A = [[2,1],[1,2]]

Characteristic polynomial det(A - λI) = (2-λ)^2 - 1 = λ^2 - 4λ + 3

Roots: λ = 1 and λ = 3

Eigenvectors: for λ=3 → v=(1,1). for λ=1 → v=(1,-1)

Algorithms: Binary search correctness idea

Invariant: target in current search interval. Each iteration halves interval; stops when found or interval empty. Complexity O(log n).

Statistics: Fit OLS simple regression — intuition & formula

Estimate slope β̂ = Cov(X,Y)/Var(X) and intercept α̂ = Ȳ - β̂ X̄. Residuals show model fit. Use train/test for evaluation to avoid overfitting.

Printable Cheat-sheets (Press Print / Export PDF)

Each mini-sheet below is formatted to print cleanly. Use your browser print dialog and choose "Save as PDF" if you want files.

Cheat: Math formula sheet

Derivatives: (d/dx) x^n = n x^{n-1}, (d/dx) sin x = cos x
Integrals: ∫ x^n dx = x^{n+1}/(n+1) + C
Common series: e^x = Σ x^n/n!, 1/(1-x)=Σ x^n

Cheat: Physics quick sheet

Newton: F=ma. Lagrangian L=T-V, Euler-Lagrange for motion.
Thermo: dU = δQ - δW; free energy G = H - T S

Cheat: CS & ML quick

Big-O cheat: O(1), O(log n), O(n), O(n log n), O(n^2)
ML: loss, gradient descent, cross-validation, regularization (L1, L2)

Flashcards — shuffle, flip, study

What is the derivative of sin x?

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Deck contents (conceptual)

derivative rules, eigenvector def, CLT idea, Bayes' rule statement, Jacobian purpose, SVD idea, Lagrangian definition, OLS slope formula

Exam-mode Quizzes

Toggle "Enter Exam Mode" to hide hints/answers and enable timer. Scores are local only.

Quiz: Math & Linear Algebra (5 Qs)

1. If A is 2x2 with eigenvalues 2 and 5, what is det(A)?

2. The Taylor series of e^x about 0 includes which term?

3. In OLS, residuals sum to?

4. Which is a necessary condition for a function to have an inverse (locally)?

5. Which matrix decomposition is useful for low-rank approximations?

Quiz: CS & Algorithms (3 Qs)

1. Binary search works on arrays that are…

2. Big-O for mergesort average case is…

3. In neural nets backprop calculates…

The Obsidian Assembly Knowledge Archive

Welcome, Initiate. Only those worthy may read, absorb, and carry forward the truths herein. Handle this knowledge with caution, for some wisdom is not meant for the unprepared.

Forbidden Knowledge

The Origins of the Assembly

The Obsidian Assembly traces back to the shadow of the First Eclipse, when knowledge of the unseen planes was first whispered to mortal ears. Only a chosen few retain the memory of these events.

Secrets of the Hidden Arts

From manipulating perception to bending the will of lesser beings, the Hidden Arts require discipline, secrecy, and a willingness to sacrifice what one once believed true.

The Language of Shadows

A cipher exists to encode and transmit our truths. Written by no mortal hand, it must be interpreted by intuition and practice, for literal translation is folly.

Rituals & Practices

Night of the Ascendant

Performed during the crescent moon, initiates gather to align their intentions with the Assembly. Candles, chants, and precise timing dictate the potency of the ritual.

Binding of the Veil

This ritual allows communication with entities from beyond. Protective wards must be set beforehand, and participants must remain unwavering in focus.

Obsidian Meditation

A practice of mental fortification. Meditate before a black mirror or reflective surface for no less than an hour. Thoughts will become malleable, perception sharpened.

Council Notes

Minutes from the Arbiter

Trust and discretion guide all decisions. Only the dedicated may access these directives. The Arbiter's word shapes the path of the Assembly.

Vessel Responsibilities

Council members act as both guardians and teachers. Each Vessel oversees specific domains, from archives to ritual execution.

Artifacts & Relics

Obsidian Mirror

Used for divination and scrying, this mirror captures fragments of the unseen world. Handle only with gloves and a clear mind.

Amulet of Whispered Truths

Allows communication with hidden entities. Activation requires a whispered phrase known only to the Arbiter.

Archives / Records

Historical Logs

Recordings of past councils, discoveries, and conflicts. These documents are key to understanding the Assembly's evolution and current strategies.

Member Contributions

Insights, experiments, and personal chronicles of members past and present. Each entry is coded to prevent unwanted disclosure.

End of Archive. Tread lightly, Initiate, for knowledge carries responsibility.