# Notes on the Web

Some of the notes here are for previous versions for the courses: *caveat lector*.

If you know of any more online notes which you find useful or if there are any broken links, please e-mail us at student.reps@maths.cam.ac.uk. Some of the notes linked from here may not be accessible from outside Cambridge or even from outside the CMS.

To view/print Postscript (.ps) or PDF (.pdf) files, you will need GhostScript and Adobe Acrobat Reader respectively.

### Examples Sheets and Lecture Notes

Most example sheets and some lecture notes are available centrally on the relevant DPMMS and DAMTP pages.

- DPMMS teaching page, including example sheets and some lecture notes for Parts IA, IB, II and III.
- DAMTP undergraduate example sheets for Parts IA, IB and II of the Maths Tripos, and for Part IB of the Natural Sciences Tripos, also including some lecture notes.
- DAMTP Part III example sheets, also including some lecture notes.
- Past examination papers, including also the MPhil in Statistical Science and Maths for NST. These should also be available in libraries.

### Lecturers' Notes and Example Sheets

#### Part IA

- Algebra and Geometry (first half) by Pater Haynes. [PDF] [PS]
- Algebra and Geometry (second half) (no proofs) by Tom Körner. [PDF] [PS] [DVI]
- Differential Equations by Stuart Dalziel.
- Calculus and Methods (first half) (no proofs) by Tom Körner. [PDF] [PS] [DVI]
- Analysis I (no proofs) by Tom Körner. [PDF] [PS] [DVI]
- Probability by Douglas Kennedy.
- Vector Calculus by Stephen Cowley. [PDF] [PS]
- Vector Calculus by Matthias Dörrzapf. [PDF]
- Vectors and Matrices by Stephen Cowley. [PDF]

#### Part IB

- Linear Mathematics by Keith Carne. [PDF] • Linear Mathematics (no proofs) by Tom Körner. [PDF] [PS] [DVI] • Linear Mathematics by Andrew Glass. [PDF]
- Rings and Modules (no proofs) by Tom Körner. [PDF] [PS] [DVI]
- Groups, Rings and Fields by Nick Shepherd-Barron. [PDF] [PS]
- Analysis II (no proofs) by Tom Körner. [PDF] [PS] [DVI]
- Metric and Topological Spaces (no proofs) by Tom Körner. [PDF] [PS] [DVI]
- Further Analysis by Keith Carne. [PDF] [PS]
- Complex Analysis by Keith Carne. [PDF] [PS]
- Geometry by Nick Shepherd-Barron. [PS] • Geometry by Keith Carne. [PDF] [PS]
- Statistics by Richard Weber. [PDF]
- Optimization by Richard Weber. [PDF] • Optimization by Yuri Suhov. • Optimization by Douglas Kennedy.
- Complex Methods (no proofs) by Tom Körner. [PDF] [PS] [DVI]
- Markov Chains by Richard Weber.
- Electromagnetism by Alan Macfarlane. [PDF] [PS]
- Special Relativity by John Stewart. [PDF] [PS]
- Quantum Mechanics by Paul Townsend. [PDF]
- Fluid Dynamics I by Michael McIntyre. • Fluid Dynamics I by Natasha Berloff.
- Numerical Analysis I by Alexei Shadrin. • Numerical Analysis I by Arieh Iserles.

#### Part II

- Representation Theory by Constantin Teleman. [PDF]
- Riemann Surfaces by Constantin Teleman. [PDF]
- Algebraic Curves by Pelham Wilson. [PDF] [PS]
- Topics in Analysis (no proofs) by Tom Körner. [PDF] [PS] [DVI]
- Functional Analysis by Graham Allan. [PS] [DVI]
- Hilbert Spaces by Graham Allan. [PS] [DVI] • Hilbert Spaces by D. J. H. (Ben) Garling. [PDF]
- Linear Analysis by Mihalis Dafermos. [PDF] [PS] • Linear Analysis (no proofs) by Tom Körner. [PDF] [PS] [DVI]
- Geometry of Group Actions by Ivan Smith.
- Geometry and Groups by Keith Carne. [PDF] [PS]
- Geometry of Surfaces by Nick Shepherd-Barron. [PDF] [PS]
- Differential Manifolds by Ivan Smith.
- Differential Geometry by Gabriel Paternain. [PDF]
- Logic, Computation and Set Theory by Tom Forster. [PS]
- Coding and Cryptography (no proofs) by Tom Körner. [PDF] [PS] [DVI]
- Probability and Measure by James Norris. [PDF] [PS] • Probability and Measure by Stefan Großkinsky. [PDF]
- Applied Probability by Frank Kelly. [PS] • Applied Probability by Yuri Suhov.
- Statistical Modelling by Pat Altham. [PDF] • Statistical Modelling by Robert Gramacy. [PDF]
- Information Theory by Yuri Suhov.
- Optimization and Control by James Norris. • Optimization and Control by Richard Weber. [PDF]
- Stochastic Financial Models by Peter Friz.
- Dynamical Systems by Peter Swinnerton-Dyer. [PDF]
- Partial Differential Equations by Mark Joshi and Tony Wasserman. [PS] • Partial Differential Equations by Tom Körner. [PDF] [PS] [DVI]
- Integrable Systems by Thanasis Fokas. [PDF] [PS]
- Classical Dynamics by David Tong. [PDF] [PS]
- Quantum Physics by Ron Horgan. [PDF] [PS]
- Statistical Physics by Ron Horgan. [PS]
- Statistical Physics and Cosmology by Gary Gibbons. [PDF] • Statistical Physics and Cosmology by Paul Townsend. [PDF]
- Electrodynamics by John Stewart.
- General Relativity by Gary Gibbons. [PDF] [PS]
- Numerical Analysis II by Arieh Iserles.

#### Part III and MPhil

- Noetherian Algebras by Konstantin Ardakov. [PDF] [PS] [DVI]
- Introduction to Banach Spaces and Algebras by Graham Allan. [PS] [DVI]
- Operators on Hilbert space by Tony Wasserman. [PS]
- The Atiyah–Singer index theorem by Tony Wasserman. [PS]
- Kac–Moody and Virasoro algebras by Tony Wasserman. [PS]
- Analysis of Operators by Tony Wasserman. [PS]
- Functional Analysis (no proofs) by Tom Körner. [PDF] [PS] [DVI]
- Banach Algebras by Graham Allan. [PS] [DVI]
- Complex Analysis (no proofs) by Tom Körner. [PDF] [PS] [DVI]
- Fourier Analysis (no proofs) by Tom Körner. [PDF] [PS] [DVI]
- Topological Groups (no proofs) by Tom Körner. [PDF] [PS] [DVI]
- Riemann Surfaces and Discrete Groups by Keith Carne.
- Pseudodifferential Operators by Mark Joshi. [PDF] [PS]
- Algebraic Methods in Combinatorics by Oleg Pikhurko. [PS]
- Differential Geometry by Mihalis Dafermos. [PDF]
- 3-manifolds by Vivien Easson. [PDF] [PS]
- Smooth four-manifolds by Tim Perutz.
- Algebraic Topology by Ivan Smith.
- Symplectic Topology by Ivan Smith.
- Birational Geometry by Caucher Birkar. [PDF]
- K-theory of Banach Algebras by Tim Gowers. [DVI]
- Restriction and Kakeya Phenomena by Ben Green.
- Set Theory and Logic by Tom Forster.
- Prime Numbers by Ben Green.
- Additive Number Theory by Ben Green.
- Introduction to Probability by Mike Tehranchi. [PDF]
- Advanced Probability by James Norris. [PDF] [PS] • Advanced Probability by Grégory Miermont. [PDF]
- Stochastic Calculus and Applications by James Norris. [PDF] [PS]
- Stochastic Loewner Evolutions by James Norris. [PDF]
- Interacting Particle Sytems by Geoffrey Grimmett. [PS]
- Optimal Investment by Mike Tehranchi.
- Applied Multivariate Analysis by Pat Altham. [PDF] [PS]
- Time Series by Richard Weber. [PDF]
- Mathematics of Operational Research by Richard Weber. [PDF]
- Algebraic Coding by Yuri Suhov.
- Quantum Information Theory by Oliver Johnson and Yuri Suhov. • Quantum Information Theory by Nilanjana Datta.
- Quantum Field Theory by David Tong. [PDF] [PS]
- Symmetry and Particle Physics by Jan Gutowski.
- Statistical Field Theory by Ron Horgan. [PDF] [PS]
- Standard Model by Hugh Osborn. [PS]
- General Relativity by John Stewart.
- Black Holes by Paul Townsend. [PDF] [PS]
- Applications of Differential Geometry to Physics by Gary Gibbons. [PDF] [PS]
- Physical Cosmology by Jochen Weller. [PS]
- Astrophysical Fluid Dynamics by Gordon Ogilvie. [PDF]
- Accretion Discs by Gordon Ogilvie.
- Large-scale Atmosphere–Ocean Dynamics by Peter Haynes. [PDF]
- Environmental Fluid Dynamics by Stuart Dalziel. [PDF]
- Classical Wave Scattering by Orsola Rath Spivack. [PDF] [PS]
- Computational Methods in Fluid Dynamics by John Hinch.
- Computer-aided Geometric Design by Malcolm Sabin.
- Approximation Theory by Alexei Shadrin.
- Numerical Solution of Differential Equations by Arieh Iserles. [PDF]

### Other Notes Relating to Cambridge Courses, including Students' LaTeXed Notes

- The Archimedeans have many lecture note links.
- Paul Metcalfe has a large collection of very good lecture notes: Part IA Discrete Mathematics, and Probability; Part IB Analysis, Further Analysis, Fluid Dynamics, Geometry, Methods, Quadratic Mathematics, and Quantum Mechanics; Part II Dynamical Systems, Dynamics of Differential Equations, Electrodynamics, Fluid Dynamics,

Foundations of Quantum Mechanics, General Relativity, Methods of Mathematical Physics, Statistical Physics, and Waves in Fluid and Solid Media. - George Weatherill has a collection of lecture notes, some typed by himself.
- Mathematicians of Pembroke have a list of links to lecture notes.
- Sergey Grigorian has typed lecture notes on Part III Applications of Differential Geometry to Physics, Supersymmetry and Extra Dimensions, and Differential Geometry.
- Prof. Wilson's notes on IIB Galois Theory [PS] [DVI].
- Notes on IIB Riemann Surfaces and Galois Theory, and some other revision notes.
- Principles of Dynamics by Colm Whelan. [PDF] [PS] [DVI].
- Stochastic Networks by Alan Bain. [PDF] [PS] [DVI]

### Other Notes

These are notes from sources outside Cambridge.

- Methods of Mathematical Physics by Mark Trodden. [PDF] [PS]
- Notes on Algebraic Topology and 3-manifolds by Allen Hatcher of Cornell.
- Notes by Vitali Liskevich of Bristol on Measure Theory [PDF] [DVI].
- Notes on Complex Analysis [PS] [PDF] [DVI] and Functional Analysis [PS] [PDF] [DVI] by Douglas N. Arnold of the IMA, Minneapolis.
- Notes by Alison Etheridge of Oxford on Probability and Mathematical Finance.
- Notes on Number Theory [PS] [PDF] by R. Heath-Brown of Oxford.
- Notes by Jim Langley of Nottingham on Real Analysis [PS] [PDF], Complex Analysis, and Advanced Complex

Analysis. - Statistics notes by Mary Lunn of Oxford.
- Notes on Special Relativity and Electromagnetism by Neil Woodhouse of Oxford, and more of the same by Lionel Mason [PS] [PDF], also of Oxford.
- Electromagnetic Theory by Chris Pope. [PDF] [PS]
- Notes by David Simms of Trinity College, Dublin, on Measure Theory, Complex Analysis and Vector Analysis, Linear Algebra, Tensors and Differentials and Representation Theory.
- Notes on Model Theory by Boris Zilber of Oxford.
- Notes by Wojtek Zakrewski of Durham on Methods/Differential Equations and on Quantum Mechanics.
- Special Relativity notes by David Hogg of New York University.
- James Milne's website contains numerous sets of notes on Algebra, particularly Algebraic Geometry and Algebraic Number Theory.
- Notes on Algebra, Topology and other areas by David Wilkins of Trinity College, Dublin.
- Abstract Algebra notes by Robert Ash of the University of Illinois at Urbana-Champaign.
- Notes by Andrew Baker of Glasgow on Algebra.
- Applications of Classical Physics by Roger Blandford and Kip Thorne.
- Quantum Field Theory by Mark Srednicki. [PDF]
- Fields by Warren Siegel.
- General Relativity by Sean Carroll.
- General Relativity notes by Petr Hadrava of the Astronomical Institute of the Academy of Sciences of the Czech Republic.
- General Relativity notes by Gerard 't Hooft of Utrecht.
- Geometry and Group Theory by Chris Pope. [PDF] [PS]
- Notes on String Theory by Enrique Alvarez and Patrick Meessen of the Universidad Autonoma, Madrid.
- Superstring Theory by Elias Kiritsis. [PDF] [PS]
- Quantum Information Theory by John Preskill.

### Other resources

*This page last modified: 16 August 2007*