MA 341 : Introduction to Number Theory

MA 341 : Introduction to Number Theory
Teacher: Rob Harron
Spring 2011
MWF 1:00pm–2:00pm
PSY B49
Discussion sessions: F 2:00pm–3:00pm in PSY B39

Textbook: Elementary Number Theory, Gareth A. Jones & J. Mary Jones

Office Hours: Mondays 2:00pm–4:00pm in my office (MCS 230)

Announcements:

First meeting: Wednesday, Jan. 19
First midterm: Wednesday, Feb. 16
No discussion session: Friday, Mar. 11
Second midterm: Monday, Mar. 28
Final exam: Saturday, May 14, 3:00pm–5:00pm

Primary sources and historical references (if you're interested):

Euclid's Elements (c. 300 BC): available online from google books: Books I–II, Books III–IX, Books X–XIII
Books VII–IX deal with number theory
Diophantus' Arithmetica (c. 300 AD): Heath's Diophantus of Alexandria, second edition is a study of Diophantus and his work; it contains a condensed form of the Arithmetica in an appendix; available on the internet archive
Āryabhaṭa's Āryabhaṭīya (499 AD): available with commentary in Clark's The Āryabhaṭīya of Āryabhaṭa (on the internet archive); contains the first known study of linear Diophantine equations
Brahmagupta's Brāhmasphuṭasiddhānta (c. 628 AD): chapter 12 studies Pythagorean triples and chapter 18 studies Diophantine equations, they are available in Colebrooke's Algebra, with Arithmetic and mensuration: from the Sanscrit of Brahmegupta and Bháscara on the internet archive
Bhaskara II's (1114–1185) Lilavati and Bijaganita: also available in Colebrooke's text
Fermat's (1601–1665) complete works are available on the internet archive (in french and latin): Vol. 1, Vol. 2, Vol. 3, Vol. 4
Euler's (1707–1783) complete works are available online, see here for his number-theoretic works (in latin)
Gauss' Disquitiones Arithmeticae (1801): available online in the original latin from the GDZ
The library has an english translation, unfortunately it is not yet in the public domain
Dickson's History of the theory of numbers (1919, 1920, 1923): available on the internet archive: Vol. 1, Vol. 2, Vol. 3