Thursday, 12 p.m. at the Meeting Room of the School of Mathematics

Here we learn number theory in a broad sense, including relevant geometric ideas, topology and Galois theory. Currently we follow selected chapters from the books:
The Fundamental Theorem of Algebra by B.Fine and G.Rosenberger
Introduction to Analytic Number Theory by K. Chandrasekharan
Essential Topology by Martin D. Crossley
Elementary Number Theory by Gareth A. Jones and J. Mary Jones
Fields and Galois Theory by John M. Howie

Talks (start at 1 p.m.)

• April 5
• Ray Allen: Fermat's Last Theorem. Method of Descent and Modularity
• March 28
• Ray Allen: Rational Points on the Unit Circle
• Ewan Dalby: Constructions with the Compass and the Ruler and Field Extensions (continuation)
• March 22
• Ewan Dalby: Numbers Constructible by the Compass and the Ruler
• March 15
• Aran Nolan: Chebyshev's Estimates for the Prime Counting Function π(x) = #{ p ≤ x } (The End)
• Padraig Condon: Some Questions Involving Graphs
• March 8
• Aran Nolan: Chebyshev's Elementary Estimates for the Asymptotics of the Prime Counting Function π(x) = #{ p ≤ x }
• Padraig Condon: Examples of Non-Planar Graphs
• February 23
• Aran Nolan: Chebyshev's Elementary Estimates for the Asymptotics of the Prime Counting Function π(x) = #{ p ≤ x }
• Padraig Condon: Vector Fields, Index and Euler Characteristics
• February 16
• Ewan Dalby: Splitting Fields of Polynomials
• Lauren Watson: Chebyshev's Elementary Estimates for the Asymptotics of the Prime Counting Function π(x) = #{ p ≤ x }
• February 9
• Lauren Watson: Chebyshev's Prime Counting Functions
• Ewan Dalby: Finite Extensions of Fields
• February 2
• Padraig Condon: Compact Sets and Extreme Value Theorem
• Padraig Condon: Euler's Theorem on V-E+F for Planar Graphs and Convex Polyhedrons. Platonic Solids.
• Aran Nolan: The Sum of Reciprocal Primes is Divergent (continuation)
• January 26
• Padraig Condon: A Freaky Topological Proof of the Infinitude of Primes
• Aran Nolan: The Sum of Reciprocal Primes is Divergent (another evidence of the infinitude of primes, this time the argument is analytic)
• January 19
• Keith Glennon: Gauss' Proof of the Fundamental Theorem of Algebra (every polynomial has a complex root)
• December 14
• Aran Nolan: Distribution of Primes
• Ewan Dalby: Uniqueness of Factorization for Polynomials and Criteria of Irreducibility
• December 7
• Lauren Watson: The Euclidean Algorithm and Solving Linear Equations in Integers
• Padraig Condon: Connected and Disconnected Topological Spaces
• November 30
• Ewan Dalby: Euclidean Domains, Uniqueness of Factorization for Gaussian Integers
Units in Real Quadratic Fields and Pell's Equation
• November 23
• Aran Nolan: Division with Remainders