### Lecture Information

Instructor: Adam Bowers

Time: 8:00-8:50 am (MWF)

Location: CENTR 105

Email: abowers

Office Hours: (click here)

TA |
Sections |
Email |
Meeting Room |
---|---|---|---|

Juan Sidrach De Cardona Mora | A01, A02 | jsidrach | APM 7421 |

Yucheng Tu | A03, A04 | y7tu | APM B412 |

All discussion sections meet on Tuesdays. (Meeting Times)

Add "@ucsd.edu" to the given username to obtain your Instructor/TA's email address.

TA Office Hours: (click here)

### Course Information

**COURSE DESCRIPTION:** This course will introduce students to the origins of many topics that they encountered during a first-year single variable calculus sequence (such as Math 20A and 20B). 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:** *Ideas of Space: Euclidean, Non-Euclidean, and Relativistic* by Jeremy Gray. Clarendon Press; second edition (September 21, 1989)

*Book description:* "[T]his volume chronologically traces the evolution of Euclidean, non-Euclidean, and relativistic theories regarding the shape of the universe. A unique, highly readable, and entertaining account, the book assumes no special mathematical knowledge. It reviews the failed classical attempts to prove the parallel postulate and provides coverage of the role of Gauss, Lobachevskii, and Bolyai in setting the foundations of modern differential geometry, which laid the groundwork for Einstein's theories of special and general relativity."

Any edition/version of the book should be fine, as far as the content goes; however, there might be differences in the exercises, so double check with the "official" version of the text.

**ADDITIONAL TEXT:** We will also be referring to Geometry: Plane and Fancy by David A. Singer. This book is published by Springer and is available to UCSD students electronically for free through SpringerLink. (In order to get the text for free, you have to access that URL either using a computer on campus or using a VPN.)

**Here are some other SpringerLink geometry texts with useful historical content:**

*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).

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

**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.]

**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 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).*Journey through Mathematics*by Enrique A. González-Velasco (2011).