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How I Study AI - Learn AI Papers & Lectures the Easy Way

Concepts11

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๐Ÿ“Linear Algebra15๐Ÿ“ˆCalculus & Differentiation10๐ŸŽฏOptimization14๐ŸŽฒProbability Theory12๐Ÿ“ŠStatistics for ML9๐Ÿ“กInformation Theory10๐Ÿ”บConvex Optimization7๐Ÿ”ขNumerical Methods6๐Ÿ•ธGraph Theory for Deep Learning6๐Ÿ”ตTopology for ML5๐ŸŒDifferential Geometry6โˆžMeasure Theory & Functional Analysis6๐ŸŽฐRandom Matrix Theory5๐ŸŒŠFourier Analysis & Signal Processing9๐ŸŽฐSampling & Monte Carlo Methods10๐Ÿง Deep Learning Theory12๐Ÿ›ก๏ธRegularization Theory11๐Ÿ‘๏ธAttention & Transformer Theory10๐ŸŽจGenerative Model Theory11๐Ÿ”ฎRepresentation Learning10๐ŸŽฎReinforcement Learning Mathematics9๐Ÿ”„Variational Methods8๐Ÿ“‰Loss Functions & Objectives10โฑ๏ธSequence & Temporal Models8๐Ÿ’ŽGeometric Deep Learning8

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๐Ÿ”ทAllโˆ‘Mathโš™๏ธAlgo๐Ÿ—‚๏ธDS๐Ÿ“šTheory

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AllBeginnerIntermediate
โš™๏ธAlgorithmIntermediate

Modular Arithmetic Pitfalls

Modular arithmetic is about working with remainders, but programming languages often return negative remainders, so always normalize with (a % MOD + MOD) % MOD.

#modular arithmetic#modular inverse#fermats little theorem+12
โˆ‘MathIntermediate

Harmonic Lemma

The Harmonic Lemma says that the values of \lfloor n/i \rfloor only change about 2\sqrt{n} times, so you can iterate those value blocks in O(\sqrt{n}) instead of O(n).

#harmonic lemma
Advanced
Filtering by:
#euler totient
#integer division trick
#block decomposition
+12
โˆ‘MathAdvanced

Pรณlya Enumeration

Pรณlya Enumeration Theorem generalizes Burnsideโ€™s Lemma by turning counting under symmetry into a polynomial substitution problem.

#pรณlya enumeration#cycle index#burnside lemma+12
โˆ‘MathAdvanced

Burnside's Lemma

Burnside's Lemma says the number of distinct objects up to a symmetry group equals the average number of objects fixed by each symmetry.

#burnside's lemma#cauchy-frobenius#polya enumeration+12
โˆ‘MathAdvanced

Primitive Roots

A primitive root modulo n is a number g that cycles through all units modulo n when you repeatedly multiply by g, so its multiplicative order equals \(\varphi(n)\).

#primitive root#multiplicative order#euler totient+10
โˆ‘MathAdvanced

Divisor Function Sums

Summing the divisor function d(i) up to n equals counting lattice points under the hyperbola xy โ‰ค n, which can be done in O(โˆšn) using floor-division blocks.

#divisor function#euler totient#mobius function+11
โˆ‘MathIntermediate

Multiplicative Functions

A multiplicative function is an arithmetic function f with f(mn) = f(m)f(n) whenever gcd(m, n) = 1.

#multiplicative function#dirichlet convolution#mobius function+12
โˆ‘MathIntermediate

Euler's Totient Function

Euler's Totient Function ฯ†(n) counts how many integers from 1 to n are coprime with n.

#euler totient#phi function#coprime count+12
โˆ‘MathIntermediate

Modular Inverse

A modular inverse of a modulo m is a number a_inv such that a ร— a_inv โ‰ก 1 (mod m).

#modular inverse#extended euclidean algorithm#fermats little theorem+12
โˆ‘MathIntermediate

Euler's Theorem

Eulerโ€™s Theorem says that if a and n are coprime, then a raised to the power ฯ†(n) is congruent to 1 modulo n.

#euler totient#euler theorem#modular exponentiation+12
โˆ‘MathIntermediate

Fast Exponentiation

Fast exponentiation (binary exponentiation) computes a^n using repeated squaring in O(log n) multiplications.

#binary exponentiation#fast power#modular exponentiation+11