Visualizing Algorithms Visualizing Algorithms

Algorithms are a fascinating use case for visualization. To visualize an algorithm, we don’t merely fit data to a chart; there is no primary dataset. Instead there are logical rules that describe behavior. This may be why algorithm visualizations are so unusual, as designers experiment with novel forms to better communicate. This is reason enough to study them.

But algorithms are also a reminder that visualization is more than a tool for finding patterns in data. Visualization leverages the human visual system to augment human intellect: we can use it to better understand these important abstract processes, and perhaps other things, too.

Scholarpedia, the peer-reviewed open-access encyclopedia, where knowledge is curated by communities of experts

Scholarpedia, the peer-reviewed open-access encyclopedia, where knowledge is curated by communities of experts

Eugene M. Izhikevich, Editor-in-Chief of Scholarpedia, the peer-reviewed open-access encyclopedia

Scholarpedia is a peer-reviewed open-access encyclopedia written and maintained by scholarly experts from around the world. Scholarpedia is inspired by Wikipedia and aims to complement it by providing in-depth scholarly treatments of academic topics.

Scholarpedia and Wikipedia are alike in many respects:

both allow anyone to propose revisions to almost any article
both are “wikis” and use the familiar MediaWiki software designed for Wikipedia
both allow considerable freedom within each article’s “Talk” pages
both are committed to the goal of making the world’s knowledge freely available to all
Nonetheless, Scholarpedia is best understood by how it is unlike most wikis, differences arising from Scholarpedia’s academic origins, goals, and audience. The most significant is Scholarpedia’s process of peer-reviewed publication: all articles in Scholarpedia are either in the process of being written by a team of authors, or have already been published and are subject to expert curation.

Prior to publication,all new articles must first receive sponsorship to validate the identity, authority, and ability of the authors who propose to write it each article undergoes scholarly peer-review, requiring public approval from at least two scholarly experts

After publication, articles appear within the Scholarpedia Journal and can be cited like any other scholarly article
the visibility of future revisions to an article is controlled by the article’s Curator, usually the article’s (most) established expert at time of publication as soon as any individual’s revision to an article is accepted, the individual joins a community of recognized (non-author) article contributors the team of article contributors may from time to time act in the Curator’s stead
when an article curator resigns or is otherwise unable to serve, a new Curator is elected

This hybrid model allows Scholarpedia articles to serve as a bridge between traditional peer-reviewed journals and more dynamic and up-to-date wikis without compromising quality or trustworthiness. It aims to remove the disincentives that discourage academics from participating in online publication and productive discussion on the topics they know best.

Akin’s Laws of Spacecraft Design

Akin’s Laws of Spacecraft Design

1. Engineering is done with numbers. Analysis without numbers is only an opinion.

2. To design a spacecraft right takes an infinite amount of effort. This is why it’s a good idea to design them to operate when some things are wrong .

3. Design is an iterative process. The necessary number of iterations is one more than the number you have currently done. This is true at any point in time.

4. Your best design efforts will inevitably wind up being useless in the final design. Learn to live with the disappointment.

5. (Miller’s Law) Three points determine a curve.

6. (Mar’s Law) Everything is linear if plotted log-log with a fat magic marker.

7. At the start of any design effort, the person who most wants to be team leader is least likely to be capable of it.

8. In nature, the optimum is almost always in the middle somewhere. Distrust assertions that the optimum is at an extreme point.

9. Not having all the information you need is never a satisfactory excuse for not starting the analysis.

10. When in doubt, estimate. In an emergency, guess. But be sure to go back and clean up the mess when the real numbers come along.

11. Sometimes, the fastest way to get to the end is to throw everything out and start over.

12. There is never a single right solution. There are always multiple wrong ones, though.

13. Design is based on requirements. There’s no justification for designing something one bit “better” than the requirements dictate.

14. (Edison’s Law) “Better” is the enemy of “good”.

15. (Shea’s Law) The ability to improve a design occurs primarily at the interfaces. This is also the prime location for screwing it up.

16. The previous people who did a similar analysis did not have a direct pipeline to the wisdom of the ages. There is therefore no reason to believe their analysis over yours. There is especially no reason to present their analysis as yours.

17. The fact that an analysis appears in print has no relationship to the likelihood of its being correct.

18. Past experience is excellent for providing a reality check. Too much reality can doom an otherwise worthwhile design, though.

19. The odds are greatly against you being immensely smarter than everyone else in the field. If your analysis says your terminal velocity is twice the speed of light, you may have invented warp drive, but the chances are a lot better that you’ve screwed up.

20. A bad design with a good presentation is doomed eventually. A good design with a bad presentation is doomed immediately.

21. (Larrabee’s Law) Half of everything you hear in a classroom is crap. Education is figuring out which half is which.

22. When in doubt, document. (Documentation requirements will reach a maximum shortly after the termination of a program.)

23. The schedule you develop will seem like a complete work of fiction up until the time your customer fires you for not meeting it.

24. It’s called a “Work Breakdown Structure” because the Work remaining will grow until you have a Breakdown, unless you enforce some Structure on it.

25. (Bowden’s Law) Following a testing failure, it’s always possible to refine the analysis to show that you really had negative margins all along.

26. (Montemerlo’s Law) Don’t do nuthin’ dumb.

27. (Varsi’s Law) Schedules only move in one direction.

28. (Ranger’s Law) There ain’t no such thing as a free launch.

29. (von Tiesenhausen’s Law of Program Management) To get an accurate estimate of final program requirements, multiply the initial time estimates by pi, and slide the decimal point on the cost estimates one place to the right.

30. (von Tiesenhausen’s Law of Engineering Design) If you want to have a maximum effect on the design of a new engineering system, learn to draw. Engineers always wind up designing the vehicle to look like the initial artist’s concept.

31. (Mo’s Law of Evolutionary Development) You can’t get to the moon by climbing successively taller trees.

32. (Atkin’s Law of Demonstrations) When the hardware is working perfectly, the really important visitors don’t show up.

33. (Patton’s Law of Program Planning) A good plan violently executed now is better than a perfect plan next week.

34. (Roosevelt’s Law of Task Planning) Do what you can, where you are, with what you have.

35. (de Saint-Exupery’s Law of Design) A designer knows that he has achieved perfection not when there is nothing left to add, but when there is nothing left to take away.

36. Any run-of-the-mill engineer can design something which is elegant. A good engineer designs systems to be efficient. A great engineer designs them to be effective.

37. (Henshaw’s Law) One key to success in a mission is establishing clear lines of blame.

38. Capabilities drive requirements, regardless of what the systems engineering textbooks say.

39. Any exploration program which “just happens” to include a new launch vehicle is, de facto, a launch vehicle program.

39. (alternate formulation) The three keys to keeping a new manned space program affordable and on schedule:
1) No new launch vehicles.
2) No new launch vehicles.
3) Whatever you do, don’t develop any new launch vehicles.

40. (McBryan’s Law) You can’t make it better until you make it work.

41. Space is a completely unforgiving environment. If you screw up the engineering, somebody dies (and there’s no partial credit because most of the analysis was right…)

The Feynman Lectures on Physics

The Feynman Lectures on Physics

The Feynman Lectures on Physics, Volume I
mainly mechanics, radiation, and heat
(single-column Table of Contents)
About the Authors
Preface to the New Millennium Edition
Feynman’s Preface

Chapter 1. Atoms in Motion
  1-1 Introduction
  1-2 Matter is made of atoms
  1-3 Atomic processes
  1-4 Chemical reactions

Chapter 2. Basic Physics
  2-1 Introduction
  2-2 Physics before 1920
  2-3 Quantum physics
  2-4 Nuclei and particles

Chapter 3. The Relation of Physics to Other Sciences
  3-1 Introduction
  3-2 Chemistry
  3-3 Biology
  3-4 Astronomy
  3-5 Geology
  3-6 Psychology
  3-7 How did it get that way?

Chapter 4. Conservation of Energy
  4-1 What is energy?
  4-2 Gravitational potential energy
  4-3 Kinetic energy
  4-4 Other forms of energy

Chapter 5. Time and Distance
  5-1 Motion
  5-2 Time
  5-3 Short times
  5-4 Long times
  5-5 Units and standards of time
  5-6 Large distances
  5-7 Short distances

Chapter 6. Probability
  6-1 Chance and likelihood
  6-2 Fluctuations
  6-3 The random walk
  6-4 A probability distribution
  6-5 The uncertainty principle

Chapter 7. The Theory of Gravitation
  7-1 Planetary motions
  7-2 Kepler’s laws
  7-3 Development of dynamics
  7-4 Newton’s law of gravitation
  7-5 Universal gravitation
  7-6 Cavendish’s experiment
  7-7 What is gravity?
  7-8 Gravity and relativity

Chapter 8. Motion
  8-1 Description of motion
  8-2 Speed
  8-3 Speed as a derivative
  8-4 Distance as an integral
  8-5 Acceleration

Chapter 9. Newton’s Laws of Dynamics
  9-1 Momentum and force
  9-2 Speed and velocity
  9-3 Components of velocity, acceleration, and force
  9-4 What is the force?
  9-5 Meaning of the dynamical equations
  9-6 Numerical solution of the equations
  9-7 Planetary motions

Chapter 10. Conservation of Momentum
  10-1 Newton’s Third Law
  10-2 Conservation of momentum
  10-3 Momentum is conserved!
  10-4 Momentum and energy
  10-5 Relativistic momentum

Chapter 11. Vectors
  11-1 Symmetry in physics
  11-2 Translations
  11-3 Rotations
  11-4 Vectors
  11-5 Vector algebra
  11-6 Newton’s laws in vector notation
  11-7 Scalar product of vectors

Chapter 12. Characteristics of Force
  12-1 What is a force?
  12-2 Friction
  12-3 Molecular forces
  12-4 Fundamental forces. Fields
  12-5 Pseudo forces
  12-6 Nuclear forces

Chapter 13. Work and Potential Energy (A)
  13-1 Energy of a falling body
  13-2 Work done by gravity
  13-3 Summation of energy
  13-4 Gravitational field of large objects

Chapter 14. Work and Potential Energy (conclusion)
  14-1 Work
  14-2 Constrained motion
  14-3 Conservative forces
  14-4 Nonconservative forces
  14-5 Potentials and fields

Chapter 15. The Special Theory of Relativity
  15-1 The principle of relativity
  15-2 The Lorentz transformation
  15-3 The Michelson-Morley experiment
  15-4 Transformation of time
  15-5 The Lorentz contraction
  15-6 Simultaneity
  15-7 Four-vectors
  15-8 Relativistic dynamics
  15-9 Equivalence of mass and energy

Chapter 16. Relativistic Energy and Momentum
  16-1 Relativity and the philosophers
  16-2 The twin paradox
  16-3 Transformation of velocities
  16-4 Relativistic mass
  16-5 Relativistic energy

Chapter 17. Space-Time
  17-1 The geometry of space-time
  17-2 Space-time intervals
  17-3 Past, present, and future
  17-4 More about four-vectors
  17-5 Four-vector algebra
Chapter 18. Rotation in Two Dimensions
  18-1 The center of mass
  18-2 Rotation of a rigid body
  18-3 Angular momentum
  18-4 Conservation of angular momentum

Chapter 19. Center of Mass; Moment of Inertia
  19-1 Properties of the center of mass
  19-2 Locating the center of mass
  19-3 Finding the moment of inertia
  19-4 Rotational kinetic energy

Chapter 20. Rotation in space
  20-1 Torques in three dimensions
  20-2 The rotation equations using cross products
  20-3 The gyroscope
  20-4 Angular momentum of a solid body

Chapter 21. The Harmonic Oscillator
  21-1 Linear differential equations
  21-2 The harmonic oscillator
  21-3 Harmonic motion and circular motion
  21-4 Initial conditions
  21-5 Forced oscillations

Chapter 22. Algebra
  22-1 Addition and multiplication
  22-2 The inverse operations
  22-3 Abstraction and generalization
  22-4 Approximating irrational numbers
  22-5 Complex numbers
  22-6 Imaginary exponents

Chapter 23. Resonance
  23-1 Complex numbers and harmonic motion
  23-2 The forced oscillator with damping
  23-3 Electrical resonance
  23-4 Resonance in nature

Chapter 24. Transients
  24-1 The energy of an oscillator
  24-2 Damped oscillations
  24-3 Electrical transients

Chapter 25. Linear Systems and Review
  25-1 Linear differential equations
  25-2 Superposition of solutions
  25-3 Oscillations in linear systems
  25-4 Analogs in physics
  25-5 Series and parallel impedances

Chapter 26. Optics: The Principle of Least Time
  26-1 Light
  26-2 Reflection and refraction
  26-3 Fermat’s principle of least time
  26-4 Applications of Fermat’s principle
  26-5 A more precise statement of Fermat’s principle
  26-6 How it works

Chapter 27. Geometrical Optics
  27-1 Introduction
  27-2 The focal length of a spherical surface
  27-3 The focal length of a lens
  27-4 Magnification
  27-5 Compound lenses
  27-6 Aberrations
  27-7 Resolving power

Chapter 28. Electromagnetic Radiation
  28-1 Electromagnetism
  28-2 Radiation
  28-3 The dipole radiator
  28-4 Interference

Chapter 29. Interference
  29-1 Electromagnetic waves
  29-2 Energy of radiation
  29-3 Sinusoidal waves
  29-4 Two dipole radiators
  29-5 The mathematics of interference

Chapter 30. Diffraction
  30-1 The resultant amplitude due to n equal oscillators
  30-2 The diffraction grating
  30-3 Resolving power of a grating
  30-4 The parabolic antenna
  30-5 Colored films; crystals
  30-6 Diffraction by opaque screens
  30-7 The field of a plane of oscillating charges

Chapter 31. The Origin of the Refractive Index
  31-1 The index of refraction
  31-2 The field due to the material
  31-3 Dispersion
  31-4 Absorption
  31-5 The energy carried by an electric wave
  31-6 Diffraction of light by a screen

Chapter 32. Radiation Damping. Light Scattering
  32-1 Radiation resistance
  32-2 The rate of radiation of energy
  32-3 Radiation damping
  32-4 Independent sources
  32-5 Scattering of light

Chapter 33. Polarization
  33-1 The electric vector of light
  33-2 Polarization of scattered light
  33-3 Birefringence
  33-4 Polarizers
  33-5 Optical activity
  33-6 The intensity of reflected light
  33-7 Anomalous refraction

Chapter 34. Relativistic Effects in Radiation
  34-1 Moving sources
  34-2 Finding the “apparent” motion
  34-3 Synchrotron radiation
  34-4 Cosmic synchrotron radiation
  34-5 Bremsstrahlung
  34-6 The Doppler effect
  34-7 The ω, k four-vector
  34-8 Aberration
  34-9 The momentum of light

Chapter 35. Color Vision
  35-1 The human eye
  35-2 Color depends on intensity
  35-3 Measuring the color sensation
  35-4 The chromaticity diagram
  35-5 The mechanism of color vision
  35-6 Physiochemistry of color vision
Chapter 36. Mechanisms of Seeing
  36-1 The sensation of color
  36-2 The physiology of the eye
  36-3 The rod cells
  36-4 The compound (insect) eye
  36-5 Other eyes
  36-6 Neurology of vision

Chapter 37. Quantum Behavior
  37-1 Atomic mechanics
  37-2 An experiment with bullets
  37-3 An experiment with waves
  37-4 An experiment with electrons
  37-5 The interference of electron waves
  37-6 Watching the electrons
  37-7 First principles of quantum mechanics
  37-8 The uncertainty principle

Chapter 38. The Relation of Wave and Particle Viewpoints
  38-1 Probability wave amplitudes
  38-2 Measurement of position and momentum
  38-3 Crystal diffraction
  38-4 The size of an atom
  38-5 Energy levels
  38-6 Philosophical implications

Chapter 39. The Kinetic Theory of Gases
  39-1 Properties of matter
  39-2 The pressure of a gas
  39-3 Compressibility of radiation
  39-4 Temperature and kinetic energy
  39-5 The ideal gas law

Chapter 40. The Principles of Statistical Mechanics
  40-1 The exponential atmosphere
  40-2 The Boltzmann law
  40-3 Evaporation of a liquid
  40-4 The distribution of molecular speeds
  40-5 The specific heats of gases
  40-6 The failure of classical physics

Chapter 41. The Brownian Movement
  41-1 Equipartition of energy
  41-2 Thermal equilibrium of radiation
  41-3 Equipartition and the quantum oscillator
  41-4 The random walk

Chapter 42. Applications of Kinetic Theory
  42-1 Evaporation
  42-2 Thermionic emission
  42-3 Thermal ionization
  42-4 Chemical kinetics
  42-5 Einstein’s laws of radiation

Chapter 43. Diffusion
  43-1 Collisions between molecules
  43-2 The mean free path
  43-3 The drift speed
  43-4 Ionic conductivity
  43-5 Molecular diffusion
  43-6 Thermal conductivity

Chapter 44. The Laws of Thermodynamics
  44-1 Heat engines; the first law
  44-2 The second law
  44-3 Reversible engines
  44-4 The efficiency of an ideal engine
  44-5 The thermodynamic temperature
  44-6 Entropy

Chapter 45. Illustrations of Thermodynamics
  45-1 Internal energy
  45-2 Applications
  45-3 The Clausius-Clapeyron equation

Chapter 46. Ratchet and pawl
  46-1 How a ratchet works
  46-2 The ratchet as an engine
  46-3 Reversibility in mechanics
  46-4 Irreversibility
  46-5 Order and entropy

Chapter 47. Sound. The wave equation
  47-1 Waves
  47-2 The propagation of sound
  47-3 The wave equation
  47-4 Solutions of the wave equation
  47-5 The speed of sound

Chapter 48. Beats
  48-1 Adding two waves
  48-2 Beat notes and modulation
  48-3 Side bands
  48-4 Localized wave trains
  48-5 Probability amplitudes for particles
  48-6 Waves in three dimensions
  48-7 Normal modes

Chapter 49. Modes
  49-1 The reflection of waves
  49-2 Confined waves, with natural frequencies
  49-3 Modes in two dimensions
  49-4 Coupled pendulums
  49-5 Linear systems

Chapter 50. Harmonics
  50-1 Musical tones
  50-2 The Fourier series
  50-3 Quality and consonance
  50-4 The Fourier coefficients
  50-5 The energy theorem
  50-6 Nonlinear responses

Chapter 51. Waves
  51-1 Bow waves
  51-2 Shock waves
  51-3 Waves in solids
  51-4 Surface waves

Chapter 52. Symmetry in Physical Laws
  52-1 Symmetry operations
  52-2 Symmetry in space and time
  52-3 Symmetry and conservation laws
  52-4 Mirror reflections
  52-5 Polar and axial vectors
  52-6 Which hand is right?
  52-7 Parity is not conserved!
  52-8 Antimatter
  52-9 Broken symmetries TDK-Lambda AC/DC-Einbaunetzteil RWS-600B-12 13.8 V/DC 50 A 600 W TDK-Lambda AC/DC-Einbaunetzteil RWS-600B-12 13.8 V/DC 50 A 600 W


3,3 V/DC / 3 A
10 W Leistung
Weitbereichseingang 85 – 265 V/AC, 300VAC für 5 Sekunden
Temperaturbereich -10 bis +70 °C
interner Lüfter


Hochwertiges, universelles Industrienetzteil für Dauerbetrieb und lange Lebensdauer. Verlängerte Herstellergarantie von 5 Jahren. Auslegung der Elektrolytkondesatoren auf 10 Jahre Lebensdauer.


Ausgangsspannung einstellbar über Poti
Sicherheit und EMV nach CE, EN/UL/CSA 60950-1, UL508, CSA C22.2 No.107.1-01., EN 55022-B, EN 55011-B, FCC-B, VCCI-B
Netzteiltyp: getaktet
Anschluss: Schraubklemmen

Technische Daten

Ausgangsstrom 1 : 50 A
Länge (Tiefe) : 190 mm
Höhe : 61 mm
Breite : 120 mm
Marke : TDK-Lambda
Kategorie : AC/DC-Einbaunetzteil
Anschluss : Schraubklemme
Typ : RWS-600B-12
Eingangsspannung (max.) : 265 V/AC
Eingangsspannung (min.) : 85 V/AC
Ausgangsstrom (max.) : 50 A
Ausgangsspannung (max.) : 13.8 V/DC
Anzahl Ausgänge : 1 x
Leistung : 600 W
Eingangsspannung : 85 V/AC bis 265 V/AC
Temperaturbereich : -10 bis 50 °C
Max. Temperatur : 50 °C
Min. Temperatur : -10 °C
Ausgangsspannung 1 : 12 V/DC
Gewicht : 1600 g

Humans of New York (HONY)

Humans of New York (HONY)

My name is Brandon and I began Humans of New York in the summer of 2010. I thought it would be really cool to create an exhaustive catalogue of New York City’s inhabitants, so I set out to photograph 10,000 New Yorkers and plot their photos on a map. I worked for several months with this goal in mind, but somewhere along the way, HONY began to take on a much different character. I started collecting quotes and short stories from the people I met, and began including these snippets alongside the photographs. Taken together, these portraits and captions became the subject of a vibrant blog. With over eight million followers on social media, HONY now provides a worldwide audience with daily glimpses into the lives of strangers in New York City. It has also become a #1 NYT bestselling book.. It’s been quite a ride so far. Feel free to follow along. Lessons From the Virginia Shooting Lessons From the Virginia Shooting

Nicholas Kristof
Human rights, women’s rights, health, global affairs.

The slaying of two journalists Wednesday as they broadcast live to a television audience in Virginia is still seared on our screens and our minds, but it’s a moment not only to mourn but also to learn lessons.

The horror isn’t just one macabre double-murder, but the unrelenting toll of gun violence that claims one life every 16 minutes on average in the United States. Three quick data points:

■ More Americans die in gun homicides and suicides every six months than have died in the last 25 years in every terrorist attack and the wars in Afghanistan and Iraq combined.

■ More Americans have died from guns in the United States since 1968 than on battlefields of all the wars in American history.

■ American children are 14 times as likely to die from guns as children in other developed countries, according to David Hemenway, a Harvard professor and author of an excellent book on firearm safety. New rules of the road in Mexico City New rules of the road in Mexico City

New rules of the road in Mexico City

By Janette Sadik-Khan, Bloomberg Associates and Kelly Larson, Bloomberg Philanthropies – AUG. 25, 2015

This week, Mayor Miguel Angel Mancera celebrated the Day of the Pedestrian by announcing strong new policies to reduce speed limits and to increase penalties for dangerous driving. In doing so, he ushered in a new era of traffic safety in Mexico City.

Mayor Mancera’s actions reflect a growing global recognition of road safety as global health crisis. Around the world, 1.24 million people die in car crashes annually, including 1,100 in Mexico City in 2012—an average of three people killed every day. According to the World Health Organization, road traffic injuries are expected to become the seventh leading cause of death globally by 2030. The tragedy is that each traffic death is preventable. As we saw in New York City over the last decade and in our ongoing work with cities around the world, lives can be saved through strong road safety laws and increased enforcement. Yet nearly 85% of nations globally don’t have adequate traffic laws to help counter traffic deaths and injuries.

Mexico City joins world class cities like New York and London in addressing the number-one killer on its streets: speeding. It may seem strange to limit speeding on roads that are frequently clogged with traffic, but statistics show that large streets account for more than 50% of the pedestrian fatalities in Mexico City. The difference in 20 km/h in speed can be the difference between life and death, which is why lowering speed limits on primary roads from 70 to 50 km/h will save lives. And even a moment of distraction can take a life, which is why texting or making calls while driving must be treated as a serious threat to the safety of everybody on the street.

The mayor’s team began the process of making streets safer by redesigning Avenida Eduardo Molina and Avenida 20 de Noviembre. Safe street designs accompany all new Metrobus lines, including accessible sidewalks, protected bicycle paths and dedicated bus lanes. In addition, dozens of dangerous intersections are being redesigned and new pedestrian crossings are now underway. Mayor Mancera has also taken the bold step of committing Mexico City to Vision Zero—and the principle that no number of traffic fatalities is acceptable.
Unfortunately, the fact that you can kill someone with your car doesn’t make people drive safer. Cities must also have adequate penalties and an enforcement system to adequately deter reckless behavior. That’s why Mayor Mancera is bringing Mexico City in line with international norms, and listening to global road safety organizations that call for fines that reflect the danger these kinds of driving pose.

New designs, new speed limits, stronger enforcement—these kinds of bold moves have made streets safer in cities around the world. They are part of a whole process of engineering, enforcement and education necessary so that generations learn that traffic deaths are not an inescapable part of daily life. Dan Boneh and Victor Shoup, A Graduate Course in Applied Cryptography Dan Boneh and Victor Shoup, A Graduate Course in Applied Cryptography

Part I: Secret key cryptography
Stream ciphers
Block ciphers
Chosen plaintext attacks
Message integrity
Message integrity from universal hashing
Message integrity from collision resistant hashing
Authenticated encryption

Part II: Public key cryptography
Public key tools
Public key encryption
Chosen ciphertext secure public-key encryption
Digital signatures
Fast signatures from one-way functions
Analysis of number theoretic assumptions
Elliptic curve cryptography and pairings
Lattice based cryptography

Part III: Protocols
Identification protocols
Signatures from identification protocols
Authenticated key exchange
Key establishment with online trusted third parties
Two-party and multi-party secure computation

Basic number theory
Basic probability theory
Basic complexity theory
Probabilistic algorithms Linear Algebra and Differential Equations Linear Algebra and Differential Equations

Double Pendulum Quantum Harmonic Oscillator Laplace Equation Data Fitting Tacoma Bridge Waves in 2D Goodwill hunting Dimension of MA coast Heat and Wave The Hydrogen Atom
Fourier Series Differential equations in the plane Nonlinear discrete dynamical system Determinants in physics Projection and Rotation Diagonalization in Politics Dataanalysis and Dow Jones Noninteger dimensions Linear algebra in art Linear algebra in mechanics