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 after 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.

Introduction. Introduction notes

1. Numerical Systems.

• 1.1. Primitive Counting.
• 1.2. Number Bases. Section 1.2 notes
• 1.3. Finger Numbers and Written Numbers. Section 1.3 notes (This section includes the ASL symbols for several numbers.)
• 1.4. Simple Grouping Systems. Section 1.4 notes (This section covers Egyptian heiroglyphic numerals, Attic Greek numerals, Roman numerals, and introduces Babylonian cuneiform numerals.)
• 1.5. Multiplicative Grouping Systems. Section 1.5 notes (This section covers the Chinese numerals.)
• 1.6. Ciphered Numeral Systems. Section 1.6 notes (This section covers Greek alphabetic numerals.)
• 1.7. Positional Numeral Systems. Section 1.7 notes (This section gives additional details on Babylonian cuneiform numerals, and covers Mayan numerals.)
• Supplement. Additional Numeral Systems. Additional Numeral Systems notes (This supplement covers Aboriginal Australian body-counting, Sumerian counters and cuneiform, Egyptian hieratic numerals, Hebrew alphabetic numerals, Sequoyah's Cherokee numerals, and Inuit Kaktovik numerals.)
• 1.8. Early Computing. Section 1.8 notes
• 1.9. The Hindu-Arabic Numeral System. Section 1.9 notes
• 1.10. Arbitrary Bases. Section 1.10 notes
• Study Guide 1

2. Babylonian and Egyptian Mathematics.

• 2.1. The Ancient Orient. Section 2.1 notes
• 2.2. Babylonia: Sources. Section 2.2 notes (This section includes biographical information on Otto Neugebauer.)
• 2.3. Babylonia: Commercial and Agrarian Mathematics. Section 2.3 notes
• 2.4. Babylonia: Geometry. Section 2.4 notes (This section includes evidence that the Babylonians knew the Pythagorean Theorem; see Note 2.4.B.)
• 2.5. Babylonia: Algebra. Section 2.5 notes (This section includes evidence that the Babylonians knew the quadratic formula; see Note 2.5.D.)
• 2.6. Babylonia: Plimpton 322. Section 2.6 notes (This section covers a clay tablet with Pythagorean triples and values of the secant function squared.)
• 2.7. Egypt: Sources and Dates. Section 2.7 notes (This section includes historical information on the Rosetta Stone.)
• 2.8. Egypt: Arithmetic and Algebra. Section 2.8 notes
• 2.9. Egypt: Geometry. Section 2.9 notes
• 2.10. Egypt: A Curious Problem in the Rhind Papyrus. Section 2.10 notes
• Study Guide 2

3. Pythagorean Mathematics.

• 3.1. Birth of Demonstrative Mathematics. Section 3.1 notes
• Supplement. Proclus's Commentary on Eudemus' History of Geometry. Proclus' Commentary on Eudemus notes
• 3.2. Pythagoras and the Pythagoreans. Section 3.2 notes (This section includes a discussion of E. T. Bell's Men of Mathematics and related books on women of mathematics.)
• 3.3. Pythagorean Arithmetic. Section 3.3 notes
• 3.4. Pythagorean Theorem and Pythagorean Triples. Section 3.4 notes
• 3.5. Discovery of Irrational Magnitudes. Section 3.5 notes
• 3.6. Algebraic Identities. Section 3.6 notes
• 3.7. Geometric Solution of Quadratic Equations. Section 3.7 notes
• 3.8. Transformation of Areas. Section 3.8 notes
• 3.9. The Regular Solids. Section 3.9 notes
• 3.10. Postulational Thinking. Section 3.10 notes
• Stugy Guide 3

4. Duplication, Trisection, and Quadrature.

• 4.1. The Period from Thales to Euclid. Section 4.1 notes (This section includes some history of Plato's Academy and a discussion of Platonism and formalism.)
• Supplement. 11.2. Zeno's Paradoxes. Section 11.2 notes (This section appears later in the book but chronologically belongs here.)
• 4.2. Lines of Mathematical Development. Section 4.2 notes
• 4.3. The Three Famous Problems. Section 4.3 notes
• 4.4. The Euclidean Tools. Section 4.4 notes (This section includes a discussion of the discontinuous plane of constructible points as a model of Euclidean geometry.)
• 4.5. Duplication of the Cube. Section 4.5 notes
• 4.6. Trisection of an Angle. Section 4.6 notes (This section includes a compass and straight edge trisection of an angle using an infinite number of bisections; see Note 4.6.F.)
• 4.7. Quadrature of the Circle. Section 4.7 notes
• 4.8. A Chronology of π. (partial) Section 4.8 notes (This section includes a partial explanation of Archimedes approximation of π based on a 96-gon; see Note 4.8.B.)
• Study Guide 4

5. Euclid and His Elements.

• Supplement. Euclid's Elements-A 2,500 Year History. Webpages for the Euclid presentation
• 5.1. Alexandria. Section 5.1 notes
• 5.2. Euclid. Section 5.2 notes
• 5.3. Euclid's "Elements". Section 5.3 notes (This section includes brief biographies of Johan Heiberg in Note 5.3.J, and of Thomas Heath in Note 5.3.K.)
• Supplement. 11.3. Eudoxus' Method of Exhaustion. Section 11.3 notes (This section appears later in the book but chronologically belongs here. It also includes a description of Eudoxus' model of planetary movement based on concentric spheres.)
• 5.4. Content of the "Elements". Section 5.4 notes (This section addresses the story that Euclid wrote the Elements just to prove there are five Platonic solids; see Note 5.4.R.)
• 5.5. The Theory of Proportion. Section 5.5 notes
• 5.6. Regular Polygons. Section 5.6 notes
• 5.7. Formal Aspect of the "Elements". Section 5.7 notes
• 5.8. Euclid's Other Works. Section 5.8 notes
• Study Guide 5

6. Greek Mathematics After Euclid.

• 6.1. Historical Setting. Section 6.1 notes (This section includes a history of Alexandria from 300 BCE to 645 CE and a history of the Library of Alexandria.)
• 6.2. Archimedes. Section 6.2 notes
• Supplement. Archimedes's Method, Part 1. Archimedes' Method notes 1
• Supplement. Archimedes's Method, Part 2. Archimedes' Method notes 2
• Supplement. The Content of Archimedes' Work, Part 1. Archimedes' Work notes 1
• Supplement. The Content of Archimedes' Work, Part 2. Archimedes' Work notes 2 (This section includes a discussion of the U.S. "billion" versus the U.K. "billion"; see Note AW2.F.)
• Supplement. Archimedes: 2,000 Years Ahead of His Time. Archimedes PowerPoint presentation and the transcript of the presentation
• Supplement. 11.4. Archimedes' Method of Equilibrium. Section 11.4 notes (This section appears later in the book but chronologically belongs here.)
• 6.3. Eratosthenes. Section 6.3 notes
• 6.4. Apollonius. Section 6.4 notes
• Supplement. Section 3.1. The Parabola. Parabola notes (This is a section of notes used in the history part of Introduction to Modern Geometry [MATH 4157/5157].)
• Supplement. Proofs of Theorems in Section 3.1. Parabola proofs in Beamer
• Supplement. Printout of the Proofs of Theorems in Section 3.1. Parabola proofs print file
• Supplement. Section 3.2. The Ellipse. Ellipse notes (This is a section of notes used in the history part of Introduction to Modern Geometry [MATH 4157/5157].)
• Supplement. Proofs of Theorems in Section 3.2. Ellipse proofs in Beamer
• Supplement. Printout of the Proofs of Theorems in Section 3.2. Ellipse proofs print file
• Supplement. Section 3.3. The Hyperbola. Hyperbola notes (This is a section of notes used in the history part of Introduction to Modern Geometry [MATH 4157/5157].)
• Supplement. Proofs of Theorems in Section 3.3. Hyperbola proofs in Beamer
• Supplement. Printout of the Proofs of Theorems in Section 3.3. Hyperbola proofs print file
• 6.5. Hipparchus, Menelaus, Ptolemy, and Greek Trigonometry. Section 6.5 notes (This section includes a brief description of The Great Books of the Western World series published by Encyclopædia Britannica, since it includes translations of original works of mathematical interest; see Note 6.5.M.)
• 6.6. Heron. Section 6.6 notes
• Supplement. The Volume of a Prismatoid. Volume of a Prismatoid notes
• 6.7. Ancient Greek Algebra. Section 6.7 notes
• 6.8. Diophantus. Section 6.8 notes
• 6.9. Pappus.
• 6.10. The Commentators.
• Supplement. Hypatia of Alexandria.

7. Chinese, Hindu, and Arabian Mathematics.

• 7.1. China: Sources and Periods.
• 7.2. China: From the Shang to the Tang.
• 7.3. China: From the Tang through the Ming.
• 7.4. China: Concluding Remarks.
• 7.5. India: General Survey.
• 7.6. India: Number Computing.
• 7.7. India: Arithmetic and Algebra.
• 7.8. India: Geometry and Trigonometry.
• 7.9. India: Contrast Between Greek and Hindu Mathematics.
• 7.10. Arabia: The Rise of Moslem Culture.
• 7.11. Arabia: Arithmetic and Algebra.
• 7.12. Arabia: Geometry and Trigonometry.
• 7.13. Arabia: Some Etymology.
• 7.14. Arabia: The Arabian Contribution.

8. European Mathematics, 500 to 1600.

• 8.1. "The Dark Ages" (The Middle Ages). Section 8.1 notes
• 8.2. The Period of Transmission. Section 8.2 notes
• 8.3. Fibonacci and the Thirteenth Century. Section 8.3 notes
• Supplement. Leonardo of Pisa (Fibonacci) and the Liber abbaci. Fibonacci and Liber abbaci notes
• 8.4. The Fourteenth Century. Section 8.4 notes
• 8.5. The Fifteenth Century. Section 8.5 notes
• Supplement. Section 5.2. Regiomontanus and Euler's Trigonometric Functions. Regiomontanus and Trig Functions notes (This is a section notes used in the history part of Introduction to Modern Geometry [MATH 4157/5157]. It includes a brief history of trigonometry.)
• Supplement. Proofs of Theorems in Section 5.2. Regiomontanus and Trig Functions proofs in Beamer (prepared in Beamer).
• Supplement. Printout of the Proofs of Theorems in Section 5.2. Regiomontanus and Trig Functions proofs print file
• 8.6. The Early Arithmetics. Section 8.6 notes (This section includes a brief biography of mathematics historian David Eugene Smith.)
• 8.7. Beginnings of Algebraic Symbolism. Section 8.7 notes
• Supplement. A History of Mathematical Symbols (up to 1600). (partial) History of Math Symbols notes
• 8.8. Cubic and Quartic Equations.
• 8.9. François Viète.
• 8.10. Other Mathematicians of the Sixteenth Century.
• Study Guide 8

Additional Chapters for History of Mathematics after 1600.

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