- How particles (like electrons) behave when they travel close to the speed of light.
Combine 2 important ideas
- Quantum Mechanics
- Theory of Relativity
- Cornerstones of Modern Physics
- Predict existence of antimatter.
- Link all of the constants of mathematics together.
Basic mathematical operations
- Mozart of Mathematics
- How circumference of a circle varies with its diameter.
- Irrational number, digits go on forever without repeating.
Einstein's Field Equation
- How the Universe works at most fundamental level.
- Changed the understanding of nature and evolution of the Universe.
- Earliest moments of creation.
- Predict the existence of black holes and gravitational waves.
- Calculate the probability that one event (A) is true, given that another event (B) is also true.
- Underlie rational thinking and decision making, rather than because of any intrinsic aesthetic appeal.
- Detect faults
- Military Defence
- Medical screening
Calculate the number of primes below a given number.
- 25 Primes between 1 and 100.
- Deeper rule governing which numbers are prime.
- Primes are controlled by zeta function
- Message security in codes
- Unlock the secrets of prime numbers
the Logistic Map
Model natural processes
- Animal grows and shrinks
- Example of Chaos History
- Great complexity may arise from very simple rules.
A "Simple" Arithmetic Progression
- A sequence of numbers separated by the same amout.
- Algorithmic Reduction
Hamilton's Quaternion Formula
- Work with complex numbers that include the square roots of negative numbers.
- Quaternion algebra
- Describe objects orientations on the screen.
- Computer graphics industry
the Wave Equation
Describe how waves behave.
- Radio Waves
Study on phenomena
- Oil prospecting
- Safety on ships
- Start from a violin string.
The Yang-Baxter Equation
- Explain mathematical theory of knots
Implications for Mathematics and physics
- Waves in shallow water
- interaction of subatomic particles
- mathematical theory of knots
- String theory
The Euler-Lagrange Equation
- Describe how a rocket would go around a black hole.
- Express classical physics simply whithin a single framework.
- Deceptively short and simple
- Shape of a soap bubble
- Main Topic 13