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Resources from the Archimedeans
The Archimedeans maintains a few (hopefully) annual publications.
advice  undergrad  prelims 
11 weeks ago by coltongrainger
Lecture notes - Part II
Pure

Galois Theory Download file
Lecturer: PMH Wilson (1999)
Source of notes: Student Reps' site
Galois Theory Download file
Lecturer: PMH Wilson (2000)
Source of notes: James Lingard's site
Representation Theory Download file
Lecturer: James Lingard — revision notes
Source of notes: James Lingard's site
Riemann Surfaces Download file
Lecturer: C Teleman (2001)
Source of notes: James Lingard's site
Differential Geometry Download file
Lecturer: Gabriel Paternain (2005)
Source of notes: Gabriel Paternain's site
Algebraic Topology Download file
Lecturer: James Lingard — revision notes
Source of notes: James Lingard's site
Combinatorics Download file
Lecturer: James Lingard — revision notes
Source of notes: James Lingard's site
Number Fields Download file
Lecturer: James Lingard — revision notes
Source of notes: James Lingard's site
Codes and Cryptography Download file
Lecturer: TW Körner (2005)
Source of notes: Prof Körner's site
Probability and Measure Download file
Lecturer: Stefan Grossinsky (2005)
Source of notes: Stefan Grossinsky's page
undergrad  math.GM  math.AT  math.RA  prelims 
11 weeks ago by coltongrainger
Lecture notes - Part IB
Part IB Lecture Notes

Analysis Download file
Lecturer: JME Hyland (1996)
Source of notes: Paul Metcalfe's site
Analysis II (old course) Download file
Lecturer: TW Körner (2001)
Source of notes: Prof Körner's site
Further Analysis Download file
Lecturer: WT Gowers (1997)
Source of notes: Paul Metcalfe's site
Further Analysis
Lecturer: TK Carne (2003)
Source of notes: TK Carne's site
Geometry (old course)
Lecturer: TK Carne (2002)
Source of notes: TK Carne's site
Geometry Download file
Lecturer: NI Shepherd-Barron (1996)
Source of notes: Paul Metcalfe's site
Groups, Rings and Fields Download file
Lecturer: James Lingard — revision notes
Source of notes: James Lingard's site
Quadratic Mathematics Download file
Lecturer: James Lingard — revision notes
Source of notes: James Lingard's site
Quadratic Mathematics Download file
Lecturer: JH Coates (1996)
Source of notes: Paul Metcalfe's site
Linear Mathematics Download file
Lecturer: AMW Glass (2002)
Source of notes: AMW Glass' site
Optimisation
Lecturer: DP Kennnedy (2005)
Source of notes: Prof Kennedy's site
Optimisation Download file
Lecturer: Yuri Suhov (2011)
Source of notes: Y Suhov's page
Optimisation Download file
Lecturer: Richard Weber (2010)
Source of notes: R Weber's Optimisation page
Optimisation Download file
Lecturer: James Lingard — revision notes
Source of notes: James Lingard's site
Numerical Analysis
Lecturer: A Shadrin (2002)
Source of notes: A Shadrin's site
Statistics Download file
Lecturer: Richard Weber
Source of notes: R Weber's Statistics page
Markov Chains
Lecturer: Richard Weber (2011)
Source of notes: Weber's Markov Chains page
Markov Chains
Lecturer: James Norris (2004)
Source of notes: Norris' Markov Chains page
Complex Methods Download file
Lecturer: GW Gibbons (2010)
Source of notes: Prof Gibbons' site
Complex Methods (old course) Download file
Lecturer: TW Körner (2002)
Source of notes: Prof Körner's site
Electromagnetism Download file
Lecturer: AJ Macfarlane (2003)
Source of notes: AJ Macfarlane's site
Electromagnetism
Lecturer: AJ Macfarlane (2004)
Source of notes: DAMTP example sheets page
Quantum Mechanics Download file
Lecturer: N Dorey (2007)
Source of notes: DAMTP example sheets page
Quantum Mechanics Download file
Lecturer: NS Manton (1996)
Source of notes: Paul Metcalfe's site
Methods Download file
Lecturer: EP Shellard (1996)
Source of notes: Paul Metcalfe's site
Methods - Download files: [Part I] [Part II] [Part III] [Part IV]
Lecturer: R Jozsa (2010)
Source of notes: DAMTP example sheets page
Fluid Dynamics Download file
Lecturer: JR Lister (1996)
Source of notes: Paul Metcalfe's site
Fluid Dynamics
Lecturer: ME McIntyre
Source of notes: ME McIntyre's site
math.HO  undergrad  teaching 
11 weeks ago by coltongrainger
Lecture notes - Part IA
Part IA Lecture Notes

Analysis I (2003) Download file
Lecturer: TW Körner
Source of notes: Prof Körner's site
Algebra and Geometry (2006) Download file
Lecturer: SJ Cowley
Source of notes: Dr Cowley's site
Algebra and Geometry (1st half, 2002) Download file
Lecturer: P Haynes
Source of notes: DAMTP example sheets page
Algebra and Geometry (2nd half, 2005) Download file
Lecturer: TW Körner
Source of notes: Prof Körner's site
Vector Calculus (2000) Download file
Lecturer: SJ Cowley
Source of notes: Dr Cowley's site
Dynamics and Relativity (2011) Download file
Lecturer: STC Siklos
Source of notes: Dr Siklos' site
Probability (1996) Download file
Lecturer: FP Kelly
Source of notes: Paul Metcalfe's site
Discrete Mathematics (1995) Download file
Lecturer: J Saxl
Source of notes: Paul Metcalfe's site
math.HO  math.GM  undergrad  teaching 
11 weeks ago by coltongrainger
A.G. Kovalev: teaching materials
Part IB: Geometry (Lent Term 2018)

examples sheet 1, sheet 2, sheet 3


Part III: Riemannian geometry (Lent Term 2017)

examples sheet 1 (updated 22 February, minor changes in q. 2, 7 and 8), sheet 2, sheet 3

the final course schedule

Last example class: Monday 8 May, 2.00-3.30pm in MR14

Past exam papers: 2012


Part III: Differential Geometry (Michaelmas Term 2014)

examples sheet 1, sheet 2, sheet 3, sheet 4

the final course schedule

skeleton notes (updated Nov-2014: minor clarification on page 2, details added on the Levi–Civita):
smooth manifolds, vector bundles, Riemannian geometry
reference card on multilinear algebra
Note. In any given year only one of the topics `geodesics' or `Riemannian submanifolds' (found in the Riemannian geometry chapter) was lectured. There were minor variations in the smooth manifolds chapter.

Past exam papers: 2014


Part II(C): Topics in Analysis (Lent Term 2014)

examples sheet 1, sheet 2, sheet 3, sheet 4


Part II(D): Differential geometry (Michaelmas Term 2010)

examples sheet 1, sheet 2, sheet 3, sheet 4

supporting materials:
Triangulations and the Euler characteristic (a picture is missing as it was drawn by hand)

A set of notes (here is a direct link to the pdf file) by Prof. Gabriel Paternain (updated 28/11/12).
a link (taken from Gabriel Paternain's notes) to a great site about minimal surfaces

An animated gif showing an isometric deformation between catenoid and helicoid (taken from Wikipedia).

Imaginary is yet another great site featuring visualizations (including curves and surfaces), with free software and the mathematics behind it.


Part IB: Analysis II (Michaelmas Term 2009)

examples sheet 1, sheet 2, sheet 3, sheet 4

supporting materials:
Term by term integration and differentiation


Part IB: Complex Analysis (Lent Term 2009)

examples sheet 1, sheet 2, sheet 3

supporting materials:
Topology in the plane, Evaluation of definite integrals: case study,


Part III: Complex Manifolds (Lent Term 2009)

examples sheet 1, sheet 2, sheet 3, sheet 4


Part II(D): Riemann Surfaces (Michaelmas Term 2007)

examples sheet 1, sheet 2, sheet 3, sheet 4

course notes (24-lecture version, pictures are missing as these were drawn by hand), updated 25-Feb-2013
math.DG  math.CA  undergrad  prelims 
11 weeks ago by coltongrainger
peter may defintion list (an outline summary of point set topology)
Topology
Topology

Reminder notes on the classification of surfaces (dvi) (pdf)
An outline summary of basic point set topology (dvi) (pdf)
Compactly generated spaces, by Gaunce Lewis (pdf)
Finite topological spaces (dvi) (pdf)
Finite spaces and simplicial complexes (dvi) (pdf)
Finite groups and finite spaces (dvi) (pdf)
A quick proof of the model axioms for Top (dvi) (pdf)


Reminder notes on the classification of surfaces (dvi) (pdf)
An outline summary of basic point set topology (dvi) (pdf)
Compactly generated spaces, by Gaunce Lewis (pdf)
Finite topological spaces (dvi) (pdf)
Finite spaces and simplicial complexes (dvi) (pdf)
Finite groups and finite spaces (dvi) (pdf)
A quick proof of the model axioms for Top (dvi) (pdf)
undergrad  math.AT  math.GT  open 
11 weeks ago by coltongrainger
QnAs with Gilbert Strang | PNAS
Of the world’s mathematicians, Gilbert Strang is possibly the most visible—or at least among the most frequently viewed. Millions of students from the Americas, Africa, China, Europe, India, and Singapore have watched Strang’s lectures on linear algebra courtesy of Massachusetts Institute of Technology (MIT)’s OpenCourseWare Web site (1), and many have e-mailed him to ask for one-on-one help. A former president of the Society for Industrial and Applied Mathematics (SIAM), author of several textbooks (2–9), and 2009 electee to the National Academy of Sciences, Strang wrote the book on linear algebra—and his text has changed how the material is taught. Strang recently spoke with PNAS about the importance of linear algebra for today’s research, as well as his recent work on the matrices used in signal processing, a branch of mathematics used to construct tools as diverse as MRI scanners, music synthesizers, and speech-to-text converters.
math.GM  undergrad 
august 2018 by coltongrainger
Abstract Algebra MATH E-222 2003 lectures
Algebra is the language of modern mathematics. This course introduces students to that language through a study of groups, group actions, vector spaces, linear algebra, and the theory of fields. In these free videotaped lectures, Professor Gross presents an array of algebraic concepts.
math.GM  undergrad 
august 2018 by coltongrainger
JIBLM Introduction to Abstract Algebra by Morrow, Margaret L.
A carefully sequenced collection of problems for an inquiry-learning approach in a one-semester Introduction to Abstract Algebra Class. The topics developed include basic notions about groups and subgroups; cyclic groups; homomorphisms and isomorphisms; and cosets. The notes culminate with the concept of quotient groups and the first isomorphism theorem. The approach is fairly elementary. A student with just a little experience with sets, functions, and elementary proof writing will be able to make substantial independent progress through the notes, particularly with the support of peers or instructor in an inquiry-based learning environment.
math.HO  math.GM  undergrad 
august 2018 by coltongrainger
JIBLM Exploring Affine Transformations by May, Jr., E. Lee
Building on a foundation of linear algebra – and, for the later chapters, real analysis -- this course introduces students to the realm of nonlinear transformations by means of affinities, which are linear translations plus a nonzero shift. Intended for advanced undergraduates and graduate students. The notes can be used for a class of several students, undergraduate or graduate, or as a guide for independent study.
math.HO  math.GM  undergrad 
august 2018 by coltongrainger
JIBLM Linear Algebra by Clark, David M.
One semester undergraduate course (omitting last chapter) or beginning graduate course (omitting first chapter) in linear algebra: vectors in 3-space, structure of finite dimentional linear spaces and inner product spaces, linear transformations.
math.HO  undergrad  math.GM 
august 2018 by coltongrainger

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