Title 200 Ideas - Exploration Number Theory Prime Number Mathematical Objects Numbers Complex Number 117.2 KB 2
```                            Maths SL & HL
202 Exploration Ideas/Topics
Algebra & Number Theory
Statistics & Modelling
Geometry
Calculus/Analysis & Functions
Probability & Probability Distributions
Games & Game Theory
Topology & Networks
Logic & Sets
Numerical Analysis
Physical, Biological & Social Sciences
Miscellaneous
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##### Document Text Contents
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Maths SL & HL
202 Exploration Ideas/Topics

Algebra & Number Theory
Modular arithmetic
Goldbach’s conjecture
Probabilistic number theory
Applications of complex numbers
Diophantine equations
Continued fractions
General solution of a cubic equation
Applications of logarithms
Polar equations
Patterns in Pascal’s triangle
Finding prime numbers
Random numbers
Pythagorean triples
Mersenne primes
Magic squares & cubes
Loci and complex numbers
Matrices and Cramer’s rule
Divisibility tests
Egyptian fractions
Complex numbers & transformations
Euler’s identity: 1 0ie   
Chinese remainder theorem
Fermat’s last theorem
Natural logarithms of complex numbers
Twin primes problem
Hypercomplex numbers
Diophantine application: Cole numbers
Odd perfect numbers
Euclidean algorithm for GCF
Palindrome numbers
Factorable sets of integers of the form ak + b
Algebraic congruences
Inequalities related to Fibonacci numbers
Combinatorics – art of counting
Boolean algebra
Graphical representation of roots of complex numbers
Roots of unity

Statistics & Modelling
Traffic flow
Logistic function and constrained growth
Modelling growth of tumours
Modelling the shape of a bird’s egg
Correlation coefficients
Central limit theorem
Modelling change in record performances for a sport
Hypothesis testing
Least squares regression
Regression to the mean
Modelling growth of computer power

Geometry
Non-Euclidean geometries
Cavalieri’s principle
Packing 2D and 3D shapes
Ptolemy’s theorem
Hexaflexagons
Heron’s formula
Geodesic domes
Proofs of Pythagorean theorem
Minimal surfaces & soap bubbles
Tesseract – a 4D cube
Map projections
Tiling the plane – tessellations
Penrose tiles
Morley’s theorem
Cycloid curve
Symmetries of spider webs
Fractal tilings
Euler line of a triangle
Fermat point for polygons & polyhedra
Pick’s theorem & lattices
Properties of a regular pentagon
Conic sections
Nine-point circle
Geometry of the catenary curve
Regular polyhedra
Euler’s formula for polyhedra
Eratosthenes’ - measuring earth’s circumference
Stacking cannon balls
Ceva’s theorem for triangles
Constructing a cone from a circle
Conic sections as loci of points
Consecutive integral triangles
Area of an ellipse
Mandelbrot set and fractal shapes
Curves of constant width
Sierpinksi triangle
Squaring the circle
Polyominoes
Reuleaux triangle
Architecture and trigonometry
Spherical geometry
Biorhythms
Wi-Fi Triangulation

Calculus/Analysis & Functions
Mean Value theorem
Torricelli’s trumpet (Gabriel’s horn)
Integrating to infinity
Applications of power series
Newton’s law of cooling
Fundamental theorem of calculus
Brachistochrone (min.time) problem
Second order differential equations
l’Hopital’s rule and evaluating limits
Hyperbolic functions