### Lecture Information

Instructor: Adam Bowers

Time: MWF 10:00a-10:50a

Location: RCLAS R73 (Remote Classroom) — This class will meet **ONLINE** only.

Discussion sections will be held on Tuesdays and will meet online. TA and section information will be posted to Canvas.

Final Exam (from the Schedule of Classes): `06/07/2021 M 8:00a-10:59a Location: TBA`

Since this class is meeting online exclusively, the following online tools will be crucial to the success of the course.

- Canvas: Learning management system
- Piazza: Online discussion forum
- Gradescope: Pen-and-paper homework submission (access through Canvas)
- Zoom: Broadcasting remote lectures (access through Canvas)

### Course Information

**COURSE DESCRIPTION:** This course will introduce students to the origins of many topics that they may encounter during a first-year mathematics course. Focus will be on the mathematical development (rather than the mathematicians themselves), but some biographical information will be given. (*Note:* Topics of Math 163 may vary from year to year.)

**REQUIRED TEXT:** Journey through Genius: The Great Theorems of Mathematics by William Dunham. Penguin Books; 1st edition (August 1, 1991).

*From the back of the book:* "Dunham places each theorem within its historical context and explores the very human and often turbulent life of the creator—from Archimedes, the absentminded theoretician whose absorption in his work often precluded eating or bathing, to Gerolamo Cardano, the sixteenth-century mathematician whose accomplishments flourished despite a bizarre array of misadventures, to the paranoid genius of modern times, Georg Cantor. He also provides step-by-step proofs for the theorems, each easily accessible to readers with no more than a knowledge of high school mathematics. A rare combination of the historical, biographical, and mathematical, Journey Through Genius is a fascinating introduction to a neglected field of human creativity."

**OTHER BOOKS:** This is a selection of well-known books on mathematics and the people behind mathematics.

**History of Calculus:**

*The History of the Calculus and Its Conceptual Development*by C. Boyer (1959).*The Calculus Gallery: Masterpieces from Newton to Lebesgue*by W. Dunham (2008).*The Historical Development of the Calculus*by C.H. Edwards, Jr. (1979).*Journey through Mathematics*by Enrique A. González-Velasco (2011).

**General History of Mathematics:**

*A History of Mathematics*by C. Boyer and U. Merzbach (2011).*Mathematics and Its History*by J. Stillwell (2010).*The Search for Certainty: A Journey Through the History of Mathematics, 1800-2000*by F.J. Swetz (editor) (2012).*The European Mathematical Awakening: A Journey Through the History of Mathematics from 1000 to 1800*by F.J. Swetz (editor) (2013).

**History of Euclidean and Non-Euclidean Geometry:**

*Non-Euclidean Geometry: A Critical and Historical Study of its Development*by R. Bonola (2010). [Originally published as*La Geometria non-Euclidea*in 1912. The older versions of this book are in the public domain, which means it can be freely downloaded from many sources. Here is a copy, for example.]*Euclidean and Non-Euclidean Geometries: Development and History*by M.J. Greenberg (2007).*The thirteen books of Euclid's Elements*by T.L. Heath (translation and commentary). [This book was originally published in 1908 and is now in the public domain, which means that it can be downloaded freely from many sources. You can get Volume I from here, for example.]*Euclid Vindicated from Every Blemish*by G. Saccheri. Translated by G.B. Halsted and L. Allegri; edited and annotated by V. De Risi. (2014). [Originally published in 1733 as*Euclides ab omni naevo vindicatus*, often translated as*Euclid Freed of Every Flaw*.]*An Axiomatic Approach to Geometry*by F. Borceux (2014).*Geometry by Its History*by A. Ostermann and G. Wanner (2012).*Geometry: Plane and Fancy*by David A. Singer (1998).