SBU 102 Topics

Notes

For some topics there is already a paper or book chapter about the topics that were assigned to each of the students.

The book Journey through genius, which can be the source for some topics, is in the Math Library.

Remember that you can choose a specific aspect of a topic to explain.

Most importantly, make sure you fully understand whatever you choose to present.

Presentations topics and papers (somewhat organized)

• Max Dehn on Hilbert's Third Problem
• The Turing Machine
• Constructible Numbers
• History of the Binomial Theorem
• History of the Quadratic Equation
• The Goldbach Conjecture
• History of Logarithms and Logarithm Tables
• Navigation and Mathematics
• Astronomy and Mathematics
• History of Measurement
• The Platonic Solids
• Mathematics and Perspective in Art
• Alicia Boole Stott and the Fourth Dimension
• History of the Fourth Dimension in Mathematics
• The Pythagorean Theorem Across Civilizations
• The Fibonacci Sequence and Nature
• The History of Prime Numbers
• The Birth of Algebra (Al-Khwarizmi)
• Boolean Algebra and the Logic of Computers
• Ada Lovelace and the First Computer Program
• Fibonacci’s Liber Abaci and How His Ideas Influenced Western Mathematics
• The Mathematical Foundations of Cryptography: A Historical Perspective
• The Bridges of Königsberg and Graph Theory
• The History of Coordinate Geometry (Descartes)
• The Development of Negative Numbers
• How the Calendar Evolved

1. History of the number e
2. The rule of false position
3. The origin of polar coordinates
4. Cavalieri's Method of Indivisible
5. The secret spiritual history of calculus
6. Historical Stages in the Definition of Curves
7. History of Platonic solids
8. History of the Euclidean Steiner tree problem
9. History of the Cycloid see also Journey through genius
10. Origin and Evolution of the Secant Method in One Dimension
11. The Lengths of Curves
12. History of the binomial theorem
13. History of the Normal Distribution
14. History of Hyperbolic Geometry
15. History of Fermat last Theorem
16. Japanese Temple Geometry
17. Gauss-Jordan Reduction: A Brief History
18. Multiplication from Lilavati to the Summa
19. Right-Angled Triangles in Ancient China
20. Tangency and Optimization without Limits
21. Fermat Last Theorem
22. Ideas of calculus in the Islamic word
23. Ideas of calculus in India
24. The beginnings of probability and the Problem of Points

Interesting people and their ideas

1. Thales and the Height of the great pyramid of Giza.
2. Archimedes and the quadrature of the parabola
3. Heron's Formula for Triangular Area Journey through genius
4. How Ptolemy constructed trigonometry tables
5. Diophantus and the birth of literal algebra
6. Omar Khayyam, mathematician
7. The Remarkable Ibn al-Haytham
8. The Algebra of Abu Kamil
9. Aryabhata and Ancient Indian methods for computing square root
10. Ramanujan's Notebooks (also The Indian Mathematician Ramanujan)
11. Saccheri on non-Euclidean geometry
12. How Kepler Discovered the Elliptical Orbit
13. The Discovery of Ceres: How Gauss Became Famous
14. Fermat on Number Theory
15. Fermat's Method of Finding Areas under Graphs. . See also Here.
16. Hamilton on the Discovery of Quaternions
17. Euler and the proof of the Fundamental Theorem of Algebra
18. Euler and the bridges of Konigsberg
19. Euler's Contribution to Number Theory see also Journey through genius
20. Cauchy and the Origins of Rigorous Calculus
21. Viète, Descartes and the Cubic Equation
22. Gauss and the Regular Polygon of Seventeen Sides
23. Gauss and the Discovery of Ceres
24. Cantor and The Non-Denumerabilty of the Continuum on Journey through genius
25. Newton and the binomial theorem, see also Journey through Genius by William Dunham.
26. The Bernoullis and the Harmonic Series, see Journey through Genius by William Dunham.