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). Online class notes are also available for History of Mathematics before 1600.

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. These notes have not been classroom tested and may have typographical errors. This is a work in progress, and links to some of the sections within this collection of notes may not work since not all sections of notes are currently available.

Howard Eves' An Introduction to the History of Mathematics, 6th edition, is over 30 year old and sometimes shows its age. These notes follow it closely in outline, but provide within the notes much extra material not in the book, as well as many supplements to the sections of notes (some used in other classes and some given as departmental seminars). Also, these notes contain more modern terminology than that used at places in the book (for example, "The Dark Ages" in the book are referred to as "The Middle Ages" in these notes). For dates, we use the notation BCE (Before the Common Era) and CE (Common Era), as opposed to the older BC (Before Christ) and AD (Anno Domini); this notation is common in the history community, though not universal. One of the major strengths of Eves' book is the "Problem Studies" exercises at the end of each chapter, and these will play a large role in the classroom use of these notes. An often-cited source throughout these notes is the MacTutor History of Mathematics website. This is maintained by Saint Andrews University in Scotland and it is a reliable reference. Another source used is Wikipedia. The material contained on the Wikipedia webpages is potentially less reliable. It is such a convenient and huge source, that it has been occasionally cited in these notes. However, it is most often used just for general historical information (which should be accurate). If academic sites are available with needed information, then attempts have been made use these references.

9. The Dawn of Modern Mathematics.

• 9.1. The Seventeenth Century.
• 9.2. Napier.
• 9.3. Logarithms.
• 9.4. The Savilian and Lucasian Professorships.
• 9.5. Harriet and Oughtred.
• 9.6. Galileo.
• 9.7. Kepler.
• 9.8. Desargues.
• 9.9. Pascal.

10. Analytic Geometry and Other Precalculus Developments.

• 10.1. Analytic Geometry.
• 10.2. Descartes.
• 10.3. Fermat.
• Supplement. Fermat's Last Theorem-History. Fermat's Last Theorem-History notes (This supplement is used in the class Elementary Number Theory [MATH 3120].)
• 10.4. Roberval and Torricelli.
• 10.5. Huygens.
• 10.6. Some Seventeenth-Century Mathematicians of France and Italy. (This section includes a history of Mersenne primes.)
• 10.7. Some Seventeenth-Century Mathematicians of Germany and the Low Countries.
• 10.8. Some Seventeenth-Century British Mathematicians.

11. The Calculus and Related Concepts.

• 11.1. Introduction.
• 11.2. Zeno's Paradoxes. Section 11.2 notes
• 11.3. Eudoxus' Method of Exhaustion. Section 11.3 notes (This section includes a description of Eudoxus' model of planetary movement based on concentric spheres.)
• 11.4. Archimedes' Method of Equilibrium. Section 11.4 notes
• 11.5. The Beginnings of Integration in Western Europe.
• 11.6. Cavaleri's Method of Indivisibles.
• 11.7. The Beginning of Differentiation.
• 11.8. Wallis and Barrow.
• 11.9. Newton.
• 11.10. Leibniz.

12. The Eighteenth Century and the Exploitation of the Calculus.

• 12.1. Introduction and Apology.
• 12.2. The Bernoulli Family.
• 12.3. De Moivre and Probability.
• 12.4. Taylor and Maclaurin.
• 12.5. Euler.
• Supplement. Leonard Euler - Happy 300th Birthday! (a celebration of the 300th anniversary of his birth). Euler presentation webpage
• 12.6. Clairaut, d'Alembert, and Lambert.
• 12.7. Agnesi and du Châtelet.
• 12.8. Lagrange.
• 12.9. Laplace and Legendre.
• 12.10. Monge and Carnot.
• 12.11. The Metric System.
• 12.12. Summary.

13. The Early Nineteenth Century and the Liberation of Geometry and Algebra.

• 13.1. The Prince of Mathematicians.
• Supplement. The Fundamental Theorem of Algebra - A History (an intuitive argument as to why the Fundamental Theorem of Algebra is true). Fundamental Theorem of Algebra - History presentation in PowerPoint
• 13.2. Germain and Somerville.
• 13.3. Fourier and Poisson.
• 13.4. Bolzano.
• 13.5. Cauchy.
• 13.6. Abel and Galois.
• Supplement. Bicentennial of Evariste Galois (a celebration of the 200th anniversary of his birth). Galois Presentation webpage
• Supplement. A Student's Question: Why The Hell Am I In This Class? (This is a quick review of the history of algebraic equations including the cubic, quartic, and unsolvability of the quintic. This supplement is used in the class Introduction to Modern Algebra [MATH 4127/5217].) A Student's Question notes
• 13.7. Jacobi and Dirichlet.
• 13.8. Non-Euclidean Geometry.
• Supplement. Hyperbolic Geometry (an axiomatic approach with a side order of history). Hyperbolic Geometry notes
• Supplement. A Quick Introduction to Non-Euclidean Geometry. Non-Euclidean Geometry notes
• 13.9. The Liberation of Geometry.
• 13.10. The Emergence of Algebraic Stucture.
• 13.11. The Liberation of Algebra.
• Supplement. Sylow Sesquicententennial (in commemoration of the 150th anniversary of the publication of Peter Ludwig Sylow's 1872 paper in which he presented his famous three theorems). Sylow presentation in PowerPoint.
• 13.12. Hamilton, Grassmann, Boole, and De Morgan.
• Supplement. The Quaternions: An Algebraic Approach (175th anniversary celebration of Sir William Rowan Hamilton's introduction of the quaternions in 1843). Quaternions presentation in PowerPoint
• 13.13. Cayley, Sylvester, and Hermite.
• 13.14. Academies, Societies, and Periodicals.

14. The Later Nineteenth Century and the Arithmetization of Analysis.

• 14.1. Sequel to Euclid.
• 14.2. Impossibility of Solving the Three Famous Problems with Euclidean Tools. Section 14.2 notes (This section includes brief biographies of Pierre Wantzel and Ferdinand von Lindemann.)
• 14.3. Compasses or Straight-edge Alone.
• 14.4. Projective Geometry.
• 14.5. Analytic Geometry.
• 14.6. N-dimensional Geometry.
• 14.7. Differential Geometry.
• 14.8. Felix Klein and the Erlanger Program.
• 14.9. The Arithmetization of Analysis.
• 14.10. Weierstrass and Riemann.
• 14.11. Cantor, Kronecker, and Poincaré.
• 14.12. Sonja Kovalevsky, Emmy Noether, and Charlotte Scott.
• 14.13. The Prime Numbers.
• Supplement. The Prime Number Theorem-History. Prime Number Theorem-History notes (This supplement is used in the class Elementary Number Theory [MATH 3120].)
• Supplement. The Riemann Hypothesis-History. Riemann Hypothesis-History notes (This supplement is used in the class Elementary Number Theory [MATH 3120].)

15. Abstraction and the Transition into the Twentieth Century.

• 15.1. Logical Shortcomings of Euclid's "Elements".
• 15.2. Axiomatics.
• 15.3. The Evolution of Some Basic Concepts.
• 15.4. Transfinite Numbers.
• 15.5. Topology.
• 15.6. Mathematical Logic.
• 15.7. Antinomies of Set Theory.
• 15.8. Philosophies of Mathematics.
• Supplement. Introduction to Math Philosophy and Meaning. Intro to Math Philosphy notes (This supplement is used in the class Great Ideas in Science 1 [BIOL 3018].)
• 15.9. Computers.
• Supplement. The Four-Colour Theorem: A History, Part 1. Four-Colour History Part 1 notes (This supplement is used in the class Graph Theory 2 [MATH 5450].)
• Supplement. The Four-Colour Theorem: A History, Part 2. Four-Colour History Part 2 notes (This supplement is used in the class Graph Theory 2 [MATH 5450].)
• 15.10. The New Math and Bourbaki.
• 15.11. The Tree of Mathematics.
• 15.12. What's Ahead?

Additional Chapters for History of Mathematics before 1600.

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