Resources 

Here we are collecting material and resources connected to the mini-courses and the professional development sessions. Some links might expire so please download the documents you are interested in.

Introduction to algebraic geometry 

• Here you find the lecture notes by Nigel Hitchin on projective geometry.

• Here you find a recap of the course with the list of topics covered and where to read more about them.

• In this folder you find 

  • Preparatory notes for a minicourse for the LMS Undergraduate summer school (July 2024)

  • Lecture notes for the course “Algebraic Curves” lectured at Imperial College in 2013 + exercise sheets+ solutions 

  • Alicia Dickenstein’s article Algebraic geometry tools in systems biology.

Introduction to Diophantine geometry

• Silverman, Tate, Rational points on Elliptic curves (Book).

• Das, Turchet, Invitation on Integral and Rational Points on curves and surfaces.

• Zannier, Lecture notes on Diophantine analysis.

• Hindry, Silverman, Diophantine Geometry (Book).

• Bombieri, Gubler, Heights in Diophantine Geometry (Book).

• Lang, Diophantine Geometry (Book).

References for Elliptic curves and cryptography 

• This is a very accessible reference: https://plus.maths.org/content/elliptic-cryptography

• Computerphile videos on Elliptic Curves: https://www.youtube.com/watch?v=NF1pwjL9-DE

• Lecture notes and Worksheets of the MIT course on Elliptic curves and cryptography.

Curves on finite fields 

• Keith Conrad's expository notes: https://kconrad.math.uconn.edu/blurbs/. 

• Joseph Silverman, Arithmetic of Elliptic Curves.

• Richard Griffon has a nice online course on curves over finite fields: https://math.richardgriffon.me/CFF1617.html. The course notes might be a bit advanced, but they are very detailed.

• Some notes from a previous summer school: https://tinyurl.com/ss-cff-2020. (These were written for first and second year PhD students, so they might be a bit terse. They also might have some typos. )

• Video on Algebraic Statistics: https://youtu.be/irVIQT2-K4I.

• Serre, Rational points on Curves over finite fields.

Introduction to number theory 

Here is a “small” list of elementary number theory books that you can check out:

•  Hardy, Wright: An Introduction to the Theory of Numbers

•  Davenport: Higher Arithmetic 

• Ireland, Rosen: A Classical Introduction to Modern Number Theory

• Stein: Elementary Number Theory: Primes, Congruences, and Secrets

• Koblitz N. - A course in number theory and cryptography

• Rosen: Elementary Number Theory and its Application

• 
  

The books of Stein and Koblitz contain also discussions about some computational aspects, if you are interested in these cases.

Introduction to Geometry of numbers 

• Here you find the lecture notes for the course.

• Olds, Lax, Davidoff, The geometry of numbers (book)

• Fröhlich, Taylor, Algebraic number theory (book)

• Cassels, Fröhlich, Algebraic number theory (book)

• Davenport, On a principle of Lipschitz (article)

• Lang, Algebraic number theory (book)

• Barroero, Widmer, Counting lattice points and o-minimal structures (article)

• Hindry, Silverman, Diophantine Geometry: An Introduction (book)

Math education 

• A great resource for Maths education is https://laraalcock.com/

• Here you can find link to various resources https://www.lms.ac.uk/policy/education

• Here is a link to the website of the Millenium Math Project – which has lots of resources https://maths.org

• In particular, NRICH has lots of activities for all age groups and resources for teachers and parents https://nrich.maths.org

• Plus maths has a lot of articles on Maths https://plus.maths.org/content/

• Some useful resources about inquiry based learning: https://www.inquirybasedlearning.org/

Sage Tutorial

• Link to the Sage installation guide: https://doc.sagemath.org/html/en/installation/index.html.

• Files from the Sage Tutorial.

Slides for Diletta's lecture 

Topics in Number Theory

Here are the slides for the course.

Here the exercise sheet.

Professional Development Session 

• List of possible resourses and opportunities.

• A very incomplete list of resources for master opportunities and further training.

• Scholarships available in the UK for Rwandan students in Education and Training.

• Scholarships available in the UK for Rwandan students in Mathematics.

• Fullbright scholarships for the US https://rw.usembassy.gov/education-culture/professional-exchanges/. 

• For other resources and announcements of future events see Diletta's website and the website of Balázs Szendroi.

• Tips for PhD Applications (focus on Algebraic Geometry).