**undergrad**189

Resources from the Archimedeans

august 2018 by coltongrainger

The Archimedeans maintains a few (hopefully) annual publications.

advice
undergrad
prelims
august 2018 by coltongrainger

Lecture notes - Part II

august 2018 by coltongrainger

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
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

august 2018 by coltongrainger

Lecture notes - Part IB

august 2018 by coltongrainger

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
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

august 2018 by coltongrainger

Lecture notes - Part IA

august 2018 by coltongrainger

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
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

august 2018 by coltongrainger

A.G. Kovalev: teaching materials

august 2018 by coltongrainger

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
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

august 2018 by coltongrainger

Courses of Christian Blatter

august 2018 by coltongrainger

analysis and engineering analysis

math.CA
undergrad
open
august 2018 by coltongrainger

peter may defintion list (an outline summary of point set topology)

august 2018 by coltongrainger

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
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)

august 2018 by coltongrainger

site:web.mit.edu/18.06/www/Essays *pdf - Google Search

august 2018 by coltongrainger

linear algebra essays under 18.06 at MIT

math.GM
undergrad
teaching
august 2018 by coltongrainger

QnAs with Gilbert Strang | PNAS

august 2018 by coltongrainger

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

august 2018 by coltongrainger

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.

august 2018 by coltongrainger

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

august 2018 by coltongrainger

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.

august 2018 by coltongrainger

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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