Veritas IB Matematik Exploration Topics

Veritas IB Math Exploration ayrıca IB math Extended Essay   IB nin en iddialı çalışmalarıdır. Bu çalışmalarda matematik üzerine  tez yazım çalışmalarıdır.  Master düzeyinde tez çalışmalarıdır.
Veritas IB Math Exploration , Extended Essay
  IB nin en zor bölümüdür. Biz bu konularda size yardım ediyoruz. Konu araştırma yazımı konularında. Ayrıca iyi konular ve projeler ile üniversite başvuru projelerine de dönüştürüyoruz.    

Algebra and 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 and cubes
Loci and complex numbers
Matrices and Cramer’s rule
Divisibility tests
Egyptian fractions
Complex numbers and transformations
Euler’s identity: ei_ + 1 = 0
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 Fermat’s little theorem
Prime number sieves
Recurrence expressions for phi (golden ratio)  

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 and 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 and polyhedra
Pick’s theorem and 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
Gyroid – a minimal surface
Geometric structure of the universe
Rigid and non-rigid geometric structures
Tangrams  

Calculus/analysis and 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 (minimum time) problem
Second order differential equations
L’Hôpital’s rule and evaluating limits
Hyperbolic functions
The harmonic series
Torus – solid of revolution
Projectile motion
Why e is base of natural logarithm function  

Statistics and modelling  
Traffic flow Logistic function and constrained growth
Modelling growth of tumours
Modelling epidemics/spread of a virus
Modelling the shape of a bird’s egg
Correlation coefficients
Central limit theorem
Modelling change in record performances for a sport
Hypothesis testing
Modelling radioactive decay
Least squares regression
Modelling the carrying capacity of the earth
Regression to the mean
Modelling growth of computer power past few decades      

Probability and probability distributions  
The Monty Hall problem
Monte Carlo simulations
Random walks
Insurance and calculating risks
Poisson distribution and queues
Determination of p by probability
Lotteries
Bayes’ theorem
Birthday paradox
Normal distribution and natural phenomena
Medical tests and probability Probability and expectation  
Games and game theory  
The prisoner’s dilemma
Sudoku Gambler’s fallacy
Poker and other card games
Knight’s tour in chess
Billiards and snooker
Zero sum games  

Discrete Math and Topology and networks  
 Knots Steiner problem Chinese postman problem
Travelling salesman problem
Königsberg bridge problem
Handshake problem
Möbius strip
Klein bottle  

Logic and sets  
Codes and ciphers
RSA
Numbery Theory and Encryption
Set theory and different ‘size’ infinities
Mathematical induction (strong)
Proof by contradiction
Zeno’s paradox of Achilles and the tortoise
Four colour map theorem  

Numerical analysis  

Linear programming
Fixed-point iteration
Methods of approximating programming
Applications of iteration
Newton’s method
Estimating size of large crowds
Generating the number e
Descartes’ rule of signs
Methods for solving differential equations  

Physical, biological and social sciences  
Radiocarbon dating
Gravity,
Orbits and escape velocity
Mathematical methods in economics
Biostatistics
Genetics
Crystallography
Computing centres of mass
Elliptical orbits
Logarithmic scales – decibel,
Richter, etc.

Miscellaneous  

Fibonacci sequence and spirals in nature
Predicting an eclipse
Change in a person’s BMI over time
Concepts of equilibrium in economics
Mathematics of the ‘credit crunch’
Branching patterns of plants
Column buckling – Euler theory  

Miscellaneous  

Paper folding
Designing bridges
Mathematics of rotating gears
Mathematical card tricks
Curry’s paradox – ‘missing’ square
Bar codes
Applications of parabolas

Music – notes, pitches, scales…
Voting systems
Flatland by Edwin Abbott
Terminal velocity
Towers of Hanoi puzzle
Photography Art of M.C. Escher
Harmonic mean
Sundials
Navigational systems
The abacus
Construction of calendars
Slide rules
Different number systems
Mathematics of juggling
Global positioning system (GPS)
Optical illusions
Origami
Napier’s bones
Celtic designs/knotwork
Design of product packaging
Mathematics of weaving              .