The mathematics
What is actually in here
Sixty-seven topics, listed in the order the book builds them rather than alphabetically — so the list reads as the ascent it is. Counting is on page 16. Reinforcement learning is on page 887. Everything between is derived, not cited.
Number and shape
Counting, then everything that follows from it.
- counting16
- addition17
- subtraction19
- multiplication21
- division25
- primes36
- fractions38
- decimal numbers42
- Euclidean geometry54
- exponentiation72
- probability77
- sets and Venn diagrams80
Functions and the calculus
Where the book stops being arithmetic.
- functions91
- trigonometric functions110
- polar coordinate system115
- area and volume116
- limit of a function118
- logarithmic function122
- differentiation, univariate128
- vectors138
- complex numbers151
- integration, univariate159
- inverse trigonometric functions174
- general quadratic functions178
- hyperbolic functions185
Probability, algebra, transforms
The machinery the rest of the book runs on.
- random variables200
- integration, multi-variable207
- differentiation, multi-variable256
- matrix algebra274
- affine transforms282
- regression284
- point projections300
- eigen-decomposition309
- Bézier curves328
- Fourier Series335
Physics
Mechanics, fields, and the very small.
- classical mechanics369
- electromagnetism407
- vector calculus407
- harmonic oscillator462
- particle physics463
Computing and information
From a transistor to a cipher.
- analog electronics531
- digital electronics536
- computer architecture549
- combinatorial optimization580
- entropy and data compression605
- error-correcting codes611
- Viterbi decoder624
- cryptography633
- networking645
- data modulation648
- linear programming655
Dynamics, light, relativity
Systems that change, and what light does.
- differential equations676
- thermodynamics689
- linear dynamics713
- optics721
- image processing730
- ray tracing749
- Lorentz-Einstein Theory of Relativity755
- Lagrangian mechanics765
Machine learning
Ending where the last three chapters end.
- machine learning781
- classification817
- decision trees838
- non-linear learning838
- feed-forward nets842
- neural nets842
- Kálmán filter882
- reinforcement learning887
The index
711 entries, hand-corrected against the final typeset pages. Search it.
Nothing under that name.
- 24 Puzzle26
- absolute permittivity414
- AC-to-DC rectifier534
- acceleration369
- acoustic wave equation773
- action-reaction373
- action-value function888
- activation function842
- adaptive filtering887
- adaptive moment estimation849
- adder542
- additive inverse614
- address of a variable550
- address space550
- affine transforms283
- air resistance377
- algebraïc field615
- algebraïc group615
- aliasing350, 752
- alpha particle471
- alternating current435
- alternating voltage435
- amount of information605
- amplification gain534
- Ampére's law426
- Ampére-Maxwell law434
- analog electronics561
- analog-to-digital converter601
- angle between two vectors140
- angle bisection56
- angle bisector theorem102
- anti-derivative159
- anti-matter463
- application-specific integrated circuit580
- arc length370
- arc length of a curve179
- arccosine function174
- Archimedean spiral115
- arcsine function174
- arctangent function175
- arithmetic coding607
- arithmetic logic unit549
- arithmetic mean243
- ASCII table546
- assembler551
- assembly instructions551
- associated Laguerre ODE485
- associated Legendre polynomials482
- atmospheric pressure397
- atomic mass468
- attention map868
- attomicroscopy729
- augmented coordinate300
- axis of rotation387
- azimuth210
- back substitution281
- batch normalization848
- Bayes' theorem199
- Bell inequality519
- Bellman equation889
- Benford's law245
- Bernoulli's rule137
- beta decay468
- beta particle468
- binary decimal numbers544
- binary division544
- binary multiplication543
- binary negation543
- binary tree574
- binding energy467, 468
- binning292
- binomial theorem99
- Biot-Savart law426
- bipolar junction transistor (BJT)534
- birthday paradox99
- black body705
- black hole757
- blackbody radiation471
- Bohr radius485
- Boltzmann constant697
- Brownian motion132
- BubbleSort80, 555
- built-in potential difference532
- buoyancy397
- Bézier curves329
- canonical correlation analysis (CCA)816
- canonical variables815
- canonical vectors815
- capacitance420
- capacitor420
- carbon dating469
- Cartesian coordinates115
- Cauchy's mean value theorem137
- Cauchy-Schwarz inequality140, 498
- ceiling47
- center of buoyancy397
- center of mass386
- central limit theorem228
- central processing unit549
- centrifugal force383
- centripetal acceleration383
- centripetal force383
- chain reaction469
- Chebyshev's inequality230
- Chinese remainder theorem618
- Cholesky decomposition289
- circle56
- circle triplets103
- circular motion383
- Clairaut's theorem419, 819
- classical momentum758
- Clausius' theorem694
- closed surface410
- code-division multiple access (CDMA)654
- coefficient of elasticity462
- collision378
- combination97
- combinatorial optimization581
- communication channel611
- compatible observables500
- complement of a graph586
- complex conjugate154
- complex roots153
- compression ratio703
- Compton effect721
- computational complexity290
- computer architecture561
- cone117
- confusion matrix823
- conic sections185
- conjugate symmetry342
- conjunction536
- conservation of angular momentum388
- conservation of momentum770
- constraint matrix657
- contextualized embedding map869
- continuity equation443
- control data flow graph578
- control theory887
- convection691
- convolution353
- convolution via FFT355
- convolutional code627
- convolutional layer855
- convolutional neural networks856
- Cooley-Tukey algorithm349
- coordinate descent803
- Coriolis acceleration383
- correlation233
- correlation matrix789
- cosecant function120
- cosine function110
- cosine theorem112
- cotangent function120
- Coulomb's law409, 472
- covariance232
- Cramer's rule278
- cross-correlation354
- cross-entropy856
- cryptographic hash642
- cumulative distribution function (CDF)201
- Curie temperature431
- curl418
- D flip-flop541
- data flow graph578
- de Casteljau's algorithm329
- de Morgan laws82
- de Morgan theorems537
- decay rate809
- decision problem582
- decision tree839
- decision variables657
- del operator376
- delta pulse function344
- demultiplexer541
- dependent variables230
- deterministic policy888
- dielectric413
- differential amplifier599
- differential equation439
- differential QPSK651
- Diffie-Hellman key exchange638
- diffraction474
- diffraction limit728
- digital inverter535
- digital signature642
- digital to analog converter601
- Dijkstra's algorithm587
- diode532
- discrete cosine transform731
- discrete Fourier transform (DFT)345
- discrete logarithm637
- disjunction536
- divergence of the gradient819
- divergence theorem411
- divisibility34
- division by zero544
- Doppler effect753, 755
- double slit experiment474
- doubling the cube182
- dowry problem273
- drift velocity440
- dropout856
- dual form806
- duality of samples and features805
- Earth's magnetic field504
- eddy current440
- edge detector445
- eigen-decomposition314
- eigenfunctions493
- eigenstate493
- eigenvalue311
- eigenvector311
- Einstein's field equations372
- elastic force462
- electrodynamics513
- electromotive force434
- electron capture467, 483, 553
- ellipse178
- embedding matrix866
- energy374
- energy of mass at rest759
- energy operator476
- energy quantization471
- energy-time uncertainty principle512
- enthalpy698
- entropy605
- equivalence principle372
- Eratosthenes' estimate of Earth's diameter100
- error function212
- error-correcting code612
- Ethernet647
- Euclidean algorithm40, 617
- Euclidean distance95
- Euler-Lagrange equation767
- expectation-maximization (EM)399, 734
- explained variance292
- extended Cholesky decomposition792
- extended Euclidean algorithm618
- far-field412
- Faraday cage441
- Faraday's law434, 435
- fast Fourier transform (FFT)349
- feasible basic solution657
- feed-forward network872
- Feistel cipher636
- Fermat's little theorem614
- ferromagnetism430
- Fibonacci sequence74
- field of view752
- field programmable gate array580
- finite field615
- first law of thermodynamics689
- fission469
- fixed-point544
- floating gate transistor552
- floating point544
- floor48
- flux410
- force as change in momentum372
- forget gate862
- forward bias533
- forward substitution290
- fourth-order Runge-Kutta method684
- fractal curve132
- frame of reference391, 755
- friction373
- frustum302
- fundamental theorem of algebra156
- fundamental theorem of calculus159, 214
- fundamental theorem of gradients454
- fusion469
- Galois field615
- Gauß law410
- Gauß law for gravity443
- Gauß-Jordan matrix inversion280
- Gauß-Markov theorem299
- Gauß-Newton method851
- Gaußian distribution699
- generalized binomial theorem216
- geometric mean243
- geometric quadratic solver246
- geometric series77
- Gilbert cell650
- global search586
- golden ratio95
- gradient376
- gradient of a scalar field419
- Gram-Schmidt process309
- graph577
- graph coloring581
- graph isomorphism problem583
- graphics processing unit580
- greatest common divisor40
- Greek alphabet66
- Green's theorem442
- greenhouse effect708
- Hadamard code652
- Hadamard product347
- Hadamard transform653
- half-life of decay809
- Hall effect440
- Hamiltonian770
- Hamiltonian cycle583
- Hamiltonian operator528
- Hamming (7,4) code612
- Hamming distance612
- harmonic oscillator463
- hash table575
- heart function187
- heat death695
- heat pump693
- heat transfer690
- Heisenberg's uncertainty principle500
- helical trajectory429
- Hermitian transpose316, 494
- Heron's formula for square root60
- Hessian matrix819
- heteroskedasticity809
- hidden layer842
- Higgs boson492
- histogram203
- Hooke's law462
- Huffman encoding611
- Huffman tree609
- hydrogen molecule529
- hyperbola183
- hysteresis431
- ideal gas691
- ideal gas law700
- identity matrix276
- incompatible observables500
- increment-only counter543
- independent set583, 584
- inductance437
- induction, proof by75
- inductor437
- inflection point134
- input gate862
- insulator413
- integer linear programming661
- integrated circuit547
- integrating factor676
- integration by parts161
- integration by substitution161
- Intel 8086 microprocessor550
- intermediate representation579
- interrupt554
- interrupt vector table554
- intrinsic spin492
- irrational numbers61
- isobaric701
- isochoric701
- isothermal701
- Jacobian matrix850
- Jensen's inequality782
- K-fold cross-validation801
- K-means clustering problem736
- Kepler's laws of planetary motion384, 386
- kernel function807
- kernel of an acoustic wave463
- kernel of the harmonic oscillator463
- kernel ridge regression808
- kernel trick807
- Kirchhoff's current law417
- Kirchhoff's laws417
- Kirchhoff's voltage law417
- Kálmán filter883
- Kálmán gain886
- l'Hôpital's rule137
- lagging features809
- Lagrange multiplier688
- Lagrange's theorem136, 635
- Lagrangian688
- Lagrangian mechanics766
- Lambert's cosine law750
- Laplacian of Gaußian741
- Laplacian operator444
- large language models873
- largest clique583, 587
- LASSO regression803
- laws of thermodynamics689
- layer normalization871
- LDU decomposition802
- learning rate841
- least common multiple40
- least-angle regression (LARS)798
- least-squares743
- length contraction757
- lensmaker's equation727
- Levenberg-Marquardt update851
- line integral371
- local extremum133
- local search586
- log-likelihood818
- log-odds818
- logistic regression817, 822
- long short-term memory (LSTM)863
- Lorentz factor756
- Lorentz force429
- Lorentz-Einstein theory of special relativity757
- low-power design562
- machine code551
- Maclaurin series215
- macroscopic entropy694
- macrostate692
- mantissa544
- Markov's inequality230
- mass defect468
- mass number469
- max-pooling layer855
- maximal independent set584
- maximum entropy605
- maximum likelihood626
- Maxwell's equations434
- mean80
- mean squared error734
- mean-pooling layer855
- mechanical advantage389
- mechanical energy463
- memoryless property206
- Mersenne prime634
- microscopic entropy697
- microstate696
- Milgram experiment220
- minimum Hamming distance612
- model of the atom472
- modulo34
- molecular dynamics513
- moment of inertia387
- momentum371
- momentum operator477, 501
- momentum space498
- Monte Carlo tree search (MCTS)894
- Moore-Penrose pseudoinverse806
- motion emf435
- multidimensional convolution738
- multiplexer541
- multiplication via FFT362
- multiplicative inverse614
- multivariate Gaußian distribution790
- mutual inductance438
- near-field412
- negative binary numbers542
- negative definite820
- negative feedback loop602
- negative numbers44
- negative sampling867
- network layer (IP)647
- neural network842
- Newton's law of gravitation372
- Newton's laws of motion371
- Newton-Raphson root finding method158, 821
- Noether's theorem770
- non-linear system654
- normal pdf213
- normalization of the wave function477
- normalized correlation379
- normalized cross-correlation360
- normalized variable213
- NP-complete problem583
- NP-hard problem583
- nuclear force467
- nullspace310
- number of primes is infinite48
- Nyquist frequency350
- objective function657
- observation model884
- Ohm's law416
- op-code551
- operational amplifier598
- optical flow858
- optical tweezers511
- ordinary differential equation (ODE)462
- orthogonal basis308
- orthonormal basis139, 308
- OSI model647
- Otto cycle703
- overfitting786
- overflow542
- overlap-add method358
- parabola181
- paramagnetism430
- partial derivative257
- partial differential equation (PDE)447, 685
- Pascal's triangle98
- path independence417
- path-averaged speed371
- Pauli exclusion principle495
- Pauli spin matrices494
- pendulum391
- permutation80
- phase comparator650
- phase locked loop (PLL)650
- phase transition690, 704
- photoelectric effect471, 721
- photon's momentum759
- pixel interpolation283
- Planck constant465, 472, 476
- Planck's radiation law707
- pn-junction532
- polar angle452
- policy head892
- polynomial complexity581
- polynomial long division157
- positive definite820
- positron463
- Poynting's theorem444
- prediction233
- preservation of momentum371
- prime factorization37, 641
- prime number36
- prime number test635
- prime number theorem634
- primitive element620
- principal component analysis315
- principal quantum number485
- principal solution174, 176
- principle of inertia371
- priority encoder601
- priority queue588
- probability density function (PDF)201
- probability distribution228
- programmable interrupt controller559
- projectile motion373
- projection methods301
- protein folding513
- proton-proton chain469
- pseudo-random number generator634
- Ptolemy's theorem245
- public-private key-pair642
- pyramid118
- Pythagorean theorem60
- Pythagorean triplet103
- quadrature phase-shift keying (QPSK)648
- quadrilateral to rectangle projection306
- quantization600
- quantizer734
- quantum mechanics513
- quantum state481
- R-squared292, 783
- radial acceleration383
- radial basis function808
- radial motion382
- radian62
- radio waves511
- radix16, 24
- radix conversion24, 27
- random access memory549
- rank-k update294
- rational number61
- Rayleigh–Jeans law706
- receptive field855
- rectified linear unit842
- recurrent neural network858
- recursive function557
- Reed-Solomon code624
- refractive indices722
- regret search585
- regularization798
- relativistic equation of motion771
- relativistic Lagrangian771
- relativistic momentum758
- repeat-bar43
- residual covariance794
- residual network (RNET)857
- reverse bias533
- reverse chain rule161
- ridge regression800
- Rolle's theorem136
- rotational kinetic energy389
- rounding a number43
- routing protocol646
- row-echelon matrix281
- row-major order571
- RSA cryptosystem641
- Rydberg constant473
- saddle point820
- sampling344
- scalar field376
- scattering angle466
- Schrödinger equation478, 528, 759
- secant function120
- second law of thermodynamics689
- second-order ODE680
- secret sharing564
- secure sockets layer (SSL)647
- self-inductance438
- shifting register543
- shoelace formula141
- shortest path in a graph587
- sieve of Eratosthenes36
- sigmoid function818
- signal-to-noise ratio735
- silicon doping532
- silicon grid531
- simplex algorithm657
- sine function110
- singular value decomposition317
- singular values318
- singularity161
- skin effect441
- slack variables657
- sliding dot product356
- Snell's law722
- soft-thresholding operator804
- softmax698, 868, 873, 892
- solenoid428
- sound and music339, 350
- spacetime momentum758
- spacetime velocity758
- specific heat capacity690
- specular reflection750
- speed369
- speed of light464, 705
- sphere118
- spherical coordinate system210, 451
- spherical harmonics482
- spherical mirror723
- spin operator494
- spin quantum number492
- spread-spectrum653
- square matrix276
- square root60
- squeeze theorem121
- stability713
- standing wave449
- star, construction96
- state transition graph625
- state-value function888
- stationary stochastic policy888
- statistical mechanics696
- Stewart's theorem246
- stochastic gradient descent845, 849
- Stokes' theorem419
- strong force466
- superposition principle681
- synchronous computation540
- syndrome621
- system of linear equations46
- tangent function120
- tangent line258
- tangent plane259
- Taylor series215
- temperature689
- terminal speed377
- ternary search655
- Thales' theorem57
- theory of general relativity757
- theory of relativity435
- third law of thermodynamics689
- time dilation757
- time-averaged speed371
- time-multiplexing554
- time-series809
- tiny encryption algorithm636
- torque388, 413
- total derivative452
- total differential257
- total relativistic energy759
- total variance292
- transfer learning873
- transformer437
- transformer block872
- transformer emf434
- transistor534
- translation invariance871
- transmission control protocol (TCP)647
- transverse wave720
- traveling salesman problem583
- trellis decoder626
- triangle55
- triangle inequality for integrals499
- triangulation654
- tunneling553
- ultra-low frequency radio-waves511
- underflow545
- uniform electric field413
- unit circle110
- unit vector138
- uranium dating469
- user datagram protocol (UDP)647
- vacuum permittivity409
- value head892
- Van der Waals equation700
- vanishing gradient859
- vaporization704
- variable selection789
- variable selection via Cholesky decomposition794
- variable separation677
- vector calculus379
- velocity369
- vertex cover583
- vibrational degrees of freedom699
- virial expansion700
- virtual photon466
- Viterbi algorithm627
- Viterbi decoder627, 651
- voltage416
- Voronoi tessellation736
- wave-particle duality471
- wavefront474
- weak force467
- weak learner839
- Wilson's theorem616
- windowing function350
- Woodbury identity295, 805
- work375
- Zener diode533
- zero-padding349
- zeroth law of thermodynamics689
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