Copies of the classnotes are on the internet in PDF format as given below. The notes and supplements may contain hyperlinks to posted webpages; the links appear in red fonts. The "Examples, Exercises, and Proofs" files were prepared in Beamer. The "Printout of Examples, Exercises, and Proofs" are printable PDF files of the Beamer slides without the pauses. These notes have not been classroom tested and may have typographical errors.

The catalog description for History of Mathematics is: "A study of mathematics and those who contributed to its development. Recommended for teachers and those desiring to expand their view of mathematics." The prerequisites are Linear Algebra (MATH 2010), Calculus 3 (MATH 2110), and Mathematical Reasoning (MATH 3000). With an eye on the highschool math curriculum, we concentrate on four topics: (1) numbers, (2) geometry, (3) equations and algebra, and (time permitting) (4) calculus.

On a personal note, I took History of Mathematics (MATH 411) from Anson "Joe" Albree (accessed 1/2/2022) in summer 1983 at Auburn University at Montgomery. Joe Albree is acknowledged in the preface of Katz's book on page xiv, along some luminous members of the history of math community, including Ivor Grattan-Guinness (author of numerous books and articles on the history of math, and founder of the journal History and Philosophy of Logic), John Stillwell (author of Mathematics and Its History), Judith Grabiner (author of The Origins of Cauchy's Rigorous Calculus), and Dirk Struik (author and editor of several books, including works on differential geometry and A Concise History of Mathematics).

Lunch at the Auburn University at Montgomery student center, spring 2006.
"Dr. Bob" and Joe Albree

1. Egypt and Mesopotamia.

• 1.1. Egypt.
• 1.2. Mesopotamia.
• 1.3. Conclusion.

2. The Beginnings of Mathematics in Greece.

• 2.1. The Earliest Greek Mathematics.
• 2.2. The Time of Plato.
• 2.3. Aristotle.

3. Euclid.

• 3.1. Introduction to the Elements.
• 3.2. Book I and the Pythagorean Theorem.
• 3.3. Book II and Geometric Algebra.
• 3.4. Circles and the Pentagon Construction.
• 3.5. Ratio and Proportion.
• 3.6. Number Theory.
• 3.7. Irrational Magnitudes.
• 3.8. Solid Geometry and the Method of Exhaustion.
• 3.9. Euclid's Data.

4. Archimedes and Apollonius.

• 4.1. Archimedes and Physics.
• 4.2. Archimedes and Numerical Calculations.
• 4.3. Archimedes and Geometry.
• 4.4. Conic Sections before Apollonius.
• 4.5. The Conics of Apollonius.

5. Mathematical Methods in Hellenistic Times.

• 5.1. Astronomy before Ptolemy.
• 5.2. Ptolemy and the Almagest.
• 5.3. Practical Mathematics.

6. The Final Chapters of Greek Mathematics.

• 6.1. Nicomachus and Elementary Number Theory.
• 6.2. Diophantus and Greek Algebra.
• 6.3. Pappus and Analysis.
• 6.4. Hypatia and the End of Greek Mathematics.

7. Ancient and Medieval China.

• 7.1. Introduction to Mathematics in China.
• 7.2. Calculations.
• 7.3. Geometry.
• 7.4. Solving Equations.
• 7.5. Indeterminate Analysis.
• 7.6. Transmission To and From China.

8. Ancient and Medieval India.

• 8.1. Introduction to Mathematics in India.
• 8.2. Calculations.
• 8.3. Geometry.
• 8.4. Equation Solving.
• 8.5. Indeterminate Analysis.
• 8.6. Combinatorics.
• 8.7. Trigonometry.
• 8.8. Transmission To and From India.

9. The Mathematics of Islam.

• 9.1. Introduction to Mathematics in Islam.
• 9.2. Decimal Arithmetic.
• 9.3. Algebra.
• 9.4. Combinatorics.
• 9.5. Geometry.
• 9.6. Trigonometry.
• 9.7. Transmission of Islamic Mathematics.

10. Mathematics in Medieval Europe.

• 10.1. Introduction to the Mathematics of Medieval Europe.
• 10.2. Geometry and Trigonometry.
• 10.3. Combinatorics.
• 10.4. Medieval Algebra.
• 10.5. The Mathematics of Kinematics.

11. Mathematics around the World.

• 11.1. Mathematics at the Turn of the Fourteenth Century.
• 11.2. Mathematics in America, Africa, and the Pacific.

12. Algebra in the Renaissance.

• 12.1. The Italian Abacists.
• 12.2. Algebra in France, Germany, England, and Portugal.
• 12.3. The Solution of the Cubic Equation.
• 12.4. Viète, Algebraic Symbolism, and Analysis.
• 12.5. Simon Stevin and Decimal Fractions.

13. Mathematical Methods in the Renaissance.

• 13.1. Perspective.
• 13.2. Navigation and Geography.
• 13.3. Astronomy and Trigonometry.
• 13.4. Logarithms.
• 13.5. Kinematics.

14. Algebra, Geometry, and Probability in the Seventeenth Century.

• 14.1. The Theory of Equations.
• 14.2. Analytic Geometry.
• 14.3. Elementary Probability.
• 14.4. Number Theory.
• 14.5. Projective Geometry.

15. The Beginnings of Calculus.

• 15.1. Tangents and Extrema.
• 15.2. Areas and Volumes.
• 15.3. Rectification of Curves and the Fundamental Theorem.

16. Newton and Leibniz.

• 16.1. Isaac Newton.
• 16.2. Gottfried Wilhelm Leibniz.
• 16.3. First Calculus Texts.

17. Analysis in the Eighteenth Century.

• 17.1. Differential Equations.
• 17.2. The Calculus of Several Variables.
• 17.3. Calculus Texts.
• 17.4. The Foundations of Calculus.

18. Probability and Statistics in the Eighteenth Century.

• 18.1. Theoretical Probability.
• 18.2. Statistical Inference.
• 18.3. Applications of Probability.

19. Algebra and Number Theory in the Eighteenth Century.

• 19.1. Algebra Texts.
• 19.2. Advances in the Theory of Equations.
• 19.3. Number Theory.
• 19.4. Mathematics in the Americas.

20. Geometry in the Eighteenth Century.

• 20.1. Clairaut and the Elements of Geometry.
• 20.2. The Parallel Postulate.
• 20.3. Analytic and Differential Geometry.
• 20.4. The Beginnings of Topology.
• 20.5. The French Revolution and Mathematics Education.

21. Algebra and Number Theory in the Nineteenth Century.

• 21.1. Number Theory.
• 21.2. Solving Algebraic Equations.
• 21.3. Symbolic Algebra.
• 21.4. Matrices and Systems of Linear Equations.
• 21.5. Groups and Fields-The Beginning of Structure.

22. Analysis in the Nineteenth Century.

• 22.1. Rigor in Analysis.
• 22.2. The Arithmetization of Analysis.
• 22.3. Complex Analysis.
• 22.4. Vector Analysis.

23. Probability and Statistics in the Nineteenth Century.

• 23.1. The Method of Least Squares and Probability Distributions.
• 23.2. Statistics and the Socail Science.
• 23.3. Statistical Graphs.

24. Geometry in the Nineteenth Century.

• 24.1. Differential Geometry.
• 24.2. Non-Euclidean Geometry.
• 24.3. Projective Geometry.
• 24.4. Graph Thoery and the Four-Color Problem.
• 24.5. Geometry in N Dimensions.
• 24.6. The Foundations of Geometry.

25. Aspects of the Twentieth Century and Beyond.

• 25.1. Set Theory: Problems and Paradoxes.
• 25.2. Topology.
• 25.3. New Ideas in Algebra.
• 25.4. The Statistical Revolution.
• 25.5. Computers and Applications.
• 25.6. Old Questions Answered.

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