[in English] Introduction to Classical Mathematics? Английский язык для математиков | Николай Вавилов (Nikolay Vavilov)

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source: Лекториум      2016年9月10日
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SPECIAL 7th European congress of Mathematics Berlin 2016.

source: Centre International de Rencontres Mathématiques   2015年8月3日

1 1:03:04 Gerd Faltings: The category MF in the semistable case
2 10:55 Interview at CIRM : Peter Scholze
3 46:01 Ingrid Bauer: Faithful actions of Gal(Q¯/Q) and change of fundamental group
4 55:21 Peter Scholze: p-adic cohomology of the Lubin-Tate tower
5 30:40 Salma Kuhlmann: Real closed fields and models of Peano arithmetic
6 55:47 Ulrike von Luxburg: Statistics on graphs and networks (II)
7 55:55 Natalia Tronko: Exact conservation laws for gyrokinetic Vlasov-Poisson equations
8 49:34 Sven Bachmann: A classification of gapped Hamiltonians in d=1
9 46:16 Christian Bär: Characteristic initial value problem for wave equations on manifolds
10 1:02:19 Peter Scholze: The Witt vector affine Grassmannian
11 15:51 Interview Pavel Exner
12 46:14 Christian Bär: Characteristic initial value problem for wave equations on manifolds
13 47:45 Jochen Blath: Genetic variability under the seed bank coalescent
14 52:18 Jan Bruinier: Classes of Heegner divisors and traces of singular moduli
15 42:59 Volker Diekert: Recognizable languages are Church-Rosser congruential
16 54:45 Peter Friz: Some examples of homogenization related rough paths
17 1:00:38 Ernst-Ulrich Gekeler: Algebraic curves with many rational points over non-prime finite fields
18 53:32 Jérémy Guéré : Mirror symmetry for singularities
19 1:06:49 Marc Levine: The rational motivic sphere spectrum and motivic Serre finiteness
20 25:24 Interview at CIRM : Endre Szemerédi, Abel Prize 2012
21 1:07:25 Heinrich Matzat: Braids and Galois groups
22 59:43 Volker Mehrmann : Extended Lagrange spaces and optimal control
23 59:52 Norbert Müller : Wrapping in exact real arithmetic
24 55:01 Hermann Schulz-Baldes: Invariants of disordered topological insulators
25 46:54 Aurélien Tellier: Plant ecology influences population genetics: the role of seed banks in [...]
26 55:04 Stefan Teufel: Peierls substitution for magnetic Bloch bands
27 1:32:07 Stephan Volkwein: POD a-posteriori error estimation for PDE constrained optimization
28 42:37 Tobias Weich: Resonance chains on Schottky surfaces
29 47:28 Dirk Werner: The Daugavet equation for Lipschitz operators
30 53:23 Sander Zwegers: Fourier coefficients of meromorphic Jacobi forms
31 36:26 Endre Szemerédi: Maximum size of a set of integers

Year 9 Maths by Norman J Wildberger

source: njwildberger      2015年5月7日
This series is aimed at Year 9 Maths students, primarily in Australia, but also beyond. The new Australian national curriculum in mathematics introduces new challenges for both students and teachers. I am aiming for a leisurely but concise overview of this curriculum, starting with a review of arithmetic with integers, fractions and decimal numbers. This series will have practice problems for students to do as they go along. It may be viewed in sequence, or dipped into for individual topics. Comments and suggestions by high school teachers are particularly valued: send me your feedback please!

34:49 10: Scientific notation II
47:31 9: Scientific notation I
30:56 8: Arithmetic and practice problems with index laws
27:50 7: Index laws, powers of 10 and negative exponents
35:36 6: Index laws and powers of 2
45:19 5: Review of arithmetic with decimals II
37:44 4: Review of decimal arithmetic I
48:14 3: Review of arithmetic with fractions II
43:45 2: Review of arithmetic with fractions I
40:42 1: Review of integer arithmetic

Elementary Mathematics (K-6) Explained by Norman J Wildberger

source: njwildberger   2017年2月28日
Feel like learning mathematics from the ground up? Here is your chance: K-6 mathematics explained intuitively but accurately in a novel way by a professional pure mathematician. We employ a step by step intuitive explanation of the main conceptual hurdles that young children meet when they start to learn mathematics.

10:44 0: Introduction
54:58 Counting using the grid plane
46:55 Arithmetic with rectangles
31:27 Number systems throughout history
42:16 The Hindu-Arabic number system
40:46 Laws of arithmetic using geometry
30:20 Fun with polyominoes
35:45 Addition and the names of numbers
24:41 Addition in practice
23:15 Multiples, and more names of numbers
26:16 Word problems using addition
35:41 Elementary projective (line) geometry
32:33 Pappus and Pascal
43:23 Logical reasoning with tic-tac-toe
26:58 The multiplication table
25:30 More multiplication: The 10x10 table
41:51 Some tricks to help with multiplication
26:27 Area problems using multiplication
30:00 The time scale of a human life
31:24 An introduction to measuring

Project MATHEMATICS!

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source: caltech      2017年3月3日
The “Project MATHEMATICS!” video series explore basic topics in high school mathematics in ways that cannot be done at the chalkboard or in a textbook. They bring mathematics to life with imaginative computer animation, live action, music, special effects, and a sense of humor.
The videos were animated by James F. Blinn, and produced by Professor Tom M. Apostol at the California Institute of Technology, Caltech, in Pasadena, CA.

Episode 1: Similarity - Project MATHEMATICS! 25:15 Episode 1. Similarity: Scaling multiplies lengths by the same factor and produces a similar figure. It preserves angles and ratios of lengths of corresponding line segments. Animation shows what happens to perimeters, areas, and volumes under scaling, with various applications from real life.
©1990 California Institute of Technology
Episode 2: The Story Of Pi - Project MATHEMATICS! 21:50
Episode 3: The Theorem Of Pythagoras - Project MATHEMATICS! 18:52
Episode 4: Sines And Cosines Part I - Project MATHEMATICS! 26:33
Episode 5: Sines And Cosines Part II - Project MATHEMATICS! 27:00
Episode 6: Sines And Cosines Part III - Project MATHEMATICS! 26:15
Episode 7: Polynomials - Project MATHEMATICS! 25:21
Episode 8: The Tunnel of Samos - Project MATHEMATICS! 27:14
Episode 9: Early History - Project MATHEMATICS! 27:56
Trailer 1: Siggraph 1988 - Project MATHEMATICS! 3:22
Trailer 2: Siggraph 1990 - Project MATHEMATICS! 6:03
Trailer 3: Siggraph 1993 - Project MATHEMATICS! 3:02

Enriching Mathematics Education (2015)

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source: matsciencechannel     2015年9月4日

Permutation pictures by S.Viswanath 1:07:38
Computing with vectors by K N Raghavan 1:13:58
Integer Solutions by C R Pranesachar 58:50
Bijection Counts by C R Pranesachar 1:20:00
Combinations with restrictions by S. Viswanath 1:17:37
Using Geogebra in mathematics classrooms by Revathy Parameswaran 1:09:11
From the Triangle inequality to the Isoperimetric inequality by S.Kesavan 53:28
Discussion session by Parameswaran Sankaran 1:18:35

Facets 2015

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source: matsciencechannel     2015年7月5日

"Mathematics, Measurement and Information Technology" by M Ram Murty 1:13:21
"Knotted or not?" by Vijay Kodiyalam 1:20:58
"Contagion: Modelling Infectious Diseases" by Gautam Menon 57:41
"Shapes and Connectivity" by Harish Seshadri 1:23:20
"Some Algorithmic questions in Finite Group Theory" by V Arvind 1:07:10
"Power and Limitations of Opinion Polls" by Rajeeva Karandikar 1:25:32
Panel discussion on "Prospects in Mathematics" 1:10:51

SPECIAL 7th European congress of Mathematics Berlin 2015.

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source: Centre International de Rencontres Mathématiques    2015年8月3日

Gerd Faltings: The category MF in the semistable case 1:03:04
Find this video and other talks given by worldwide mathematicians on CIRM's Audiovisual Mathematics Library: http://library.cirm-math.fr. And discover all its functionalities:
- Chapter markers and keywords to watch the parts of your choice in the video
- Videos enriched with abstracts, bibliographies, Mathematics Subject Classification
- Multi-criteria search by author, title, tags, mathematical area
For smooth schemes the category $MF$ (defined by Fontaine for DVR's) realises the "mysterious functor", and provides natural systems of coeffients for crystalline cohomology. We generalise it to schemes with semistable singularities. The new technical features consist mainly of different methods in commutative algebra.
Recording during the thematic meeting: ''Arithmetic geometry, representation theory and applications'' the June 22, 2015 at the Centre International de Rencontres Mathématiques (Marseille, France)
Filmmaker: Pascal Vichi Video editing: Guillaume Hennenfent
Interview at CIRM : Peter Scholze 10:55
Ingrid Bauer: Faithful actions of Gal(Q¯/Q) and change of fundamental group 46:01
Peter Scholze: p-adic cohomology of the Lubin-Tate tower 55:21
Salma Kuhlmann: Real closed fields and models of Peano arithmetic 30:40
Ulrike von Luxburg: Statistics on graphs and networks (II) 55:47
Natalia Tronko: Exact conservation laws for gyrokinetic Vlasov-Poisson equations 55:55
Sven Bachmann: A classification of gapped Hamiltonians in d=1 49:34
Christian Bär: Characteristic initial value problem for wave equations on manifolds 46:16
Peter Scholze: The Witt vector affine Grassmannian 1:02:19
Interview Pavel Exner 15:51
Christian Bär: Characteristic initial value problem for wave equations on manifolds 46:14
Jochen Blath: Genetic variability under the seed bank coalescent 47:45
Jan Bruinier: Classes of Heegner divisors and traces of singular moduli 52:18
Volker Diekert: Recognizable languages are Church-Rosser congruential 42:59
Peter Friz: Some examples of homogenization related rough paths 54:45
Ernst-Ulrich Gekeler: Algebraic curves with many rational points over non-prime finite fields 1:00:38
Jérémy Guéré : Mirror symmetry for singularities 53:32
Marc Levine: The rational motivic sphere spectrum and motivic Serre finiteness 1:06:49
Interview at CIRM : Endre Szemerédi, Abel Prize 2012 25:24
Heinrich Matzat: Braids and Galois groups 1:07:25
Volker Mehrmann : Extended Lagrange spaces and optimal control 59:43
Norbert Müller : Wrapping in exact real arithmetic 59:52
Hermann Schulz-Baldes: Invariants of disordered topological insulators 55:01
Aurélien Tellier: Plant ecology influences population genetics: the role of seed banks in [...] 46:54
Stefan Teufel: Peierls substitution for magnetic Bloch bands 55:04
Stephan Volkwein: POD a-posteriori error estimation for PDE constrained optimization 1:32:07
Tobias Weich: Resonance chains on Schottky surfaces 42:37
Dirk Werner: The Daugavet equation for Lipschitz operators 47:28
Sander Zwegers: Fourier coefficients of meromorphic Jacobi forms 53:23
Endre Szemerédi: Maximum size of a set of integers 36:26

Enriching Mathematics Education 2014

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source: matsciencechannel     2014年10月17日

Linear Programming by Dr. Meena Mahajan 1:20:46
Number theory and its applications by Dr. Kotyada Srinivas 1:25:50
Permutations and Combinations by Dr.Sankaran Viswanath 1:24:02
An invitation to geometry by Anirban Mukhopadhyay 1:13:26
Lines, planes and beyond : An invitation to geometry by Dr.Anirban Mukhopadhyay(Contd..) 54:35
Number theory and its applications by Kotyada Srinivas(Contd..) 1:19:41
Calculus by Dr. Sankaran Viswanath 1:28:17
Group Discussion by Parameswaran Sankaran 1:20:48

Enriching Collegiate Mathematics

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source: matsciencechannel    2014年3月20日

Linear Algebra by Prof.Amritanshu Prasad Part I 1:05:17
Linear Algebra by prof. Amritanshu Prasad Part II 1:04:55
Algebra by Prof. Vijay Kodiyalam 1:18:07
Galois Theory by Prof.Parameswaran Sankaran 1:14:52
Complex Analysis by Prof.Anirban Mukhipadhyay Part I 1:18:16
Complex Analysis by Prof.Anirban Mukhipadhyay Part II 1:21:27

Mathematics: Aspects, Prospects, and a bit of History

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source: matsciencechannel    2013年7月26日

001 Registration, Inauguration & "On the spectrum of the Laplacian" by S. Kesavan 1:12:41
002 The cakravala method for solving quadratic indeterminate equations by M D. Srinivas 1:07:51
003 "Shapes and geometry of surfaces" by Mahan Mj 1:05:27
004 "From linear algebra to robotic arm design via Groebner bases" by Manoj Kummini 1:05:07
005 Panel discussion: Prospects in Mathematics by Jugal Verma 1:05:07
006 "Panel discussion: Prospects in Mathematics" by Rajeeva Karandikar 18:39
007 Panel discussion: Prospects in Mathematics" by Ramanujam 19:18
008 "Determinant and Permanent" by Partha Mukhopadhyay 1:05:42
009 Imagine a sky filled with stars by T E Venkata Balaji 53:55
010 "Using online resources to learn Mathematics" by Amritanshu Prasad 1:13:45

S. K. Ray: Mathematics ( IIT Kanpur)

# playlist of the 32 videos (click the up-left corner of the video)

source: nptelhrd    2008年1月29日
Lecture series on Mathematics-1 by Prof S. K. Ray, Department of Mathematics and Statistics. IIT Kanpur. For more details on NPTEl, visit http://nptel.iitm.ac.in

Lecture 1 - Real Number 57:00
Lecture 2 - Sequences I 54:49
Lecture 3 - Sequences II 44:03
Lecture 4 - Sequences III 52:03
Lecture 5 - Continuous Function 55:10
Lecture 6 - Properties of Continuous function 1:01:05
Lecture 7 - Uniform Continuity 59:47
Lecture 8 - Differentiable function 55:22
Lecture 9 - Mean Value Theorems 50:19
Lecture 10 - Maxima - Minima 54:45
Lecture 11 -Taylor's Theorem 53:10
Lecture 12 - Curve Sketching 46:05
Lecture 13 - Infinite Series I 53:53
Lecture 14 - Infinite Series II 51:26
Lecture 15 - Tests of Convergence 55:48
Lecture 16 - Power Series 53:20
Lecture 17 - Riemann integral 53:44
Lecture 18 - Riemann Integrable functions 59:43
Lecture 19 - Applications of Riemann Integral 52:05
Lecture 20 - Length of a curve 57:53
Lecture 21 - Line integrals 56:21
Lecture 22 - Functions of several variables 56:23
Lecture 23 - Differentiation 1:00:20
Lecture 24 - Derivatives 55:21
Lecture 25 - Mean Value Theorem 52:03
Lecture 26 - Maxima Minima 57:10
Lecture 27 - Method of Lagrange Multipliers 50:02
Lecture 28 - Multiple Integrals 52:17
Lecture 29 - Surface Integrals 59:55
Lecture 30 - Green's Theorem 52:34
Lecture 31 - Stokes Theorem 53:57
Lecture 32 - Gauss Divergence Theorem 36:42

Lewis Carroll: Mathematics

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source: University of Oxford    2010年10月25日
Mathematics Lectures from Oxford University
The annual Oxford University Alumni Weekend aims to showcase the Collegiate University as a whole, giving prominence to a range of current research and its application to real world situations, as well as recognising the achievements of Oxford men and women. Past themes include "A Global Oxford" (2008), "Equal Citizenship" (2009) and "Shared Treasures" (2010).

Lewis Carroll in Numberland 1:11:50
Marcus du Sautoy - OUMNH 150th Anniversary Lectures 51:08
001 Introduction to Quantum Mechanics, Probability Amplitudes and Quantum States 44:05
002 Dirac Notation and the Energy Representation 42:36
003 Operators and Measurement 49:12
004 Commutators and Time Evolution (the Time Dependent Schrodinger Equation) 54:32
005 Further TDSE and the Position Representation 49:44
006 Wavefunctions for Well Defined Momentum 51:12
007 Back to Two-Slit Interference, Generalization to Three Dimensions and the Virial Theorem 52:47
008 The Harmonic Oscillator and the Wavefunctions of its Stationary States 52:01
009 Dynamics of Oscillators and the Anharmonic Oscillator 52:15
010 Transformation of Kets, Continuous and Discrete Transformations and the Rotation Operator 50:31
011 Transformation of Operators and the Parity Operator 49:23
012 Angular Momentum and Motion in a Magnetic Field 46:27
013 Hilary: The Square Well 52:31
014 A Pair of Square Wells and the Ammonia Maser 54:34
015 Tunnelling and Radioactive Decay 44:22
016 Composite Systems - Entanglement and Operators 51:29
017 Einstein-Podolski-Rosen Experiment and Bell's Inequality 51:30
018 Angular Momentum 42:28
019 Diatomic Molecules and Orbital Angular Momentum 43:52
020 Further Orbital Angular Momentum, Spectra of L2 and LZ 46:29
021 Even further Orbital Angular Momentum - Eigenfunctions, Parity and Kinetic Energy 52:10
022 Spin Angular Momentum 49:45
023 Spin 1/2 , Stern - Gerlach Experiment and Spin 1 49:23
024 Classical Spin and Addition of Angular Momenta 51:59
025 Hydrogen part 1 51:08
026 Hydrogen part 2 Emission Spectra 48:47
027 Hydrogen part 3 Eigenfunctions 50:40
Computation and the Future of Mathematics 51:51

Tanuja Srivastava: Mathematics - II (IIT Roorkee)

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source: nptelhrd    2010年4月27日
Lecture series on Mathematics-II by Dr.Tanuja Srivastava, Department of Mathematics, IIT Roorkee. For more details on NPTEL visit http://nptel.iitm.ac.in

Mod-1 Lec-1 Complex Integration 53:35
Mod-1 Lec-2 Contour Integration 1:00:46
Mod-1 Lec-3 Cauchy's Integral Theorem 49:43
Mod-1 Lec-4 Cauchy`s Integral Formula 55:18
Mod-1 Lec-5 Application of Cauchy Integral Formula 56:06
Mod-1 Lec-6 Zeros, Singularities and Poles 55:42
Mod-1 Lec-7 Residue Integration Method 50:03
Mod-1 Lec-8 Residue Theorem 1:00:59
Mod-1 Lec-9 Evaluation of Real Integrals 45:43
Mod-1 Lec-10 Evaluation of Real Improper Integrals-1 58:32
Mod-1 Lec-11 Evaluation of Real Improper Integrals-2 50:04
Mod-1 Lec-12 Evaluation of Real Improper Integrals-3 53:08
Mod-1 Lec-13 Evaluation of Real Improper Integrals-4 52:53
Mod-1 Lec-14 Evaluation of Real Integrals-Revision 1:01:56
Mod-2 Lec-1 Matrix Algebra Part - 1 50:15
Mod-2 Lec-2 Matrix Algebra Part - 2 59:42
Mod-2 Lec-3 Determinants Part - 1 54:16
Mod-2 Lec- 4 Determinants Part - 2 57:37
Mod-2 Lec-5 Solution of System Equation 1:02:12
Mod-2 Lec-6 Linear Algebra Part-1 54:40
Mod-2 Lec-7 Linear Algebra part - 2 55:48
Mod-2 Lec-8 Linear Algebra Part - 3 54:51
Mod-2 Lec-9 Linear Algebra Part - 4 54:09
Mod-2 Lec-10 Inner Product 54:08
Mod-2 Lec-11 Linear Transformation Part - 1 55:29
Mod-2 Lec-12 Linear Transformation Part - 2 52:49
Mod-2 Lec-13 Eigenvalues & Eigenvectors Part - 1 55:26
Mod-2 Lec-14 Eigenvalues & Eigenvectors Part - 2 56:46
Mod-2 Lec-15 Quadratic Forms 1:01:50
Mod-2 Lec-16 Diagonalization Part - 1 57:09
Mod-2 Lec-17 Diagonalization Part - 2 1:02:40
Mod-2 Lec-18 Solution of System of Linear Equation 40:48
Mod-2 Lec-19 Functions of Complex Variables Part - 1 55:22
Mod-2 Lec-20 Functions of Complex Variables Part - 2 1:03:17
Mod-2 Lec-21 Taylor Series 50:57
Mod-2 Lec-22 Laurent Series 53:14
Mod-2 Lec-23 Rank of a Matrix 59:21
Mod-3 Lec-1 Complex Numbers&Their Geometrical Representation 51:29

P. N. Agrawal: Mathematics - III (IIT Roorkee)

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source: nptelhrd    2009年6月25日
Lecture Series on Mathematics - III by Dr. P. N. Agrawal, Department of Mathematics, IIT Roorkee. For more details on NPTEL visit http://nptel.iitm.ac.in

Mod-1 Lec-1 Solution of ODE of First Order and First Degree 53:50
Mod-1 Lec-2 Linear Differential Equations of the First Order and Orthogonal Trajectories 50:03
Mod-1 Lec-3 Approximate Solution of An Initial Value 49:50
Mod-1 Lec-4 Series Solution of Homogeneous Linear Differential Equations-I 1:01:15
Mod-1 Lec-5 Series Solution of Homogeneous Linear Differential Equations-II 50:56
Mod-1 Lec-6 Bessel Functions and Their Properties-I 51:10
Mod-1 Lec-7 Bessel Functions And Their Properties-II 52:32
Mod-1 Lec-8 Laplace Transformation-I 53:26
Mod-1 Lec-9 Laplace Transformation-II 55:58
Mod-1 Lec-10 Applications of Laplace Transformation-I 59:53
Mod-1 Lec-11 Applications of Laplace Transformation-II 59:23
Mod-1 Lec-12 One Dimensional Wave Equation 54:08
Mod-1 Lec-13 One Dimensional Heat Equation 55:28
Mod-2 Lec-1 Introduction to Differential Equation 55:51
Mod-2 Lec-2 First Order Differential Equations and Their Geometric Interpretation 1:04:03
Mod-2 Lec-3 Differential Equations of First Order&Higher Degree 42:25
Mod-2 Lec-4 Linear Differential Equation of Second Order-Part-1 1:02:08
Mod-2 Lec-5 Linear Differential equation of Second Order-Part-2 1:04:12
Mod-2 Lec-6 Euler-Cauchy Theorem 53:00
Mod-2 Lec-7 Higher Order Linear Differential Equations 57:24
Mod-2 Lec-8 Higher Order Non Homogeneous Linear Equations 54:48
Mod-2 Lec-9 Boundary Value Problems 51:37
Mod-2 Lec-10 Strum Liouville boundary Value Problem 46:04
Mod-2 Lec-11 Fourier Series-Part-1 56:42
Mod-2 Lec-12 Fourier Series-Part-2 49:08
Mod-2 Lec-13 Convergence of the Fourier Series 56:41
Mod-2 Lec-14 Fourier Integrals 48:18
Mod-2 Lec-15 Fourier Transforms 53:11
Mod-2 Lec-16 Partial Differential Equation 54:58
Mod-2 Lec-17 First Order Partial Differential Equation 56:38
Mod-2 Lec-18 Second Order Partial Differential Equations-I 55:25
Mod-2 Lec-19 Second Order Partial Differential Equations-II 1:00:01
Mod-2 Lec-20 Solution of One Dimensional Wave Equation 48:21
Mod-2 Lec-21 Solution of Homogeneous&Non Homogeneous Equations 57:17
Mod-2 Lec-22 Fourier Integral&Transform Method for Heat Equation 58:25
Mod-2 Lec-23 Three Dimensional Laplace Equation 52:53
Mod-2 Lec-24 Solution of Drichlet Problem 47:07
Mod-2 Lec-25 Numerical Method for Laplace Poisson Equation 44:31
Mod-2 Lec-26 ADI Method for Laplace and Poisson Equation 56:39

Mathematics - Mathematical Analysis--Joel Feinstein / U of Nottingham

# automatic playing for the 38 videos (click the up-left corner for the list)

source: University of Nottingham    上次更新日期：2014年6月24日
This module introduces mathematical analysis building upon the experience of limits of sequences and properties of real numbers and on calculus. It includes limits and continuity of functions between Euclidean spaces, differentiation and integration. A variety of very important new concepts are introduced by investigating the properties of numerous examples, and developing the associated theory, with a strong emphasis on rigorous proof. This module is suitable for study at undergraduate level 2. Dr Joel Feinstein is an Associate Professor in Pure Mathematics at the University of Nottingham. After reading mathematics at Cambridge, he carried out research for his doctorate at Leeds. He held a postdoctoral position in Leeds for one year, and then spent two years as a lecturer at Maynooth (Ireland) before taking up a permanent position at Nottingham. His main research interest is in functional analysis, especially commutative Banach algebras. Dr Feinstein has published two case studies on his use of IT in the teaching of mathematics to undergraduates. In 2009, Dr Feinstein was awarded a University of Nottingham Lord Dearing teaching award for his popular and successful innovations in this area.
Additional materials for this module are available at: http://unow.nottingham.ac.uk/resources/resource.aspx?hid=... and
http://itunesu.nottingham.ac.uk/albums/71.rss
See also Dr Feinstein's blog at http://explainingmaths.wordpress.com/.

Workshop 1:  22:54
Revision Quiz :  21:23
Lecture 1:  46:56
Lecture 2a: properties of the Euclidian norm 18:19
Lecture 2b: open balls and closed balls 19:11
Workshop 2: Why do we do proofs? 30:40
Lecture 3: Bounded sets 45:16
Lecture 4a: Examples of bounded and unbounded d-cells 18:19
Lecture 4b: Bounded and unbounded d-cells continued 23:20
Workshop 3: Examples Class 1 25:45
Lecture 5: Interior and non-interior points 33:28
Lecture 6: interior points/ non-interior points 42:40
How do we do proofs? Part I - Dr Joel Feinstein 28:54
Lecture 7: Topology of d-dimensional Euclidian space 37:15
Lecture 8a: Closed sets 29:10
Lecture 8b: Sequences in d-dimensional Euclidian Space 8:10
Lecture 9: Absorption of sequences by sets 40:43
Workshop 5: Examples Class 2 24:00
Lecture 10a: Proof of the sequence criterion for closedness 26:13
Lecture 10b: Subsequences and Sequential Compactness 14:59
How do we do proofs? Part II - Dr Joel Feinstein 25:58
Lecture 11: Subsequences of sequences 44:46
Lecture 12a: Proof of Bolzano-Weierstrass theorem 36:56
Lecture 12b: Functions, Limits and Continuity 9:10
Lecture 13a: Continuation of Functions, Limits and Continuity 27:53
Lecture 13b: Continuous Functions 14:52
Lecture 14a: Sequence definition of continuity 32:20
Lecture 14b: Further theory of function limits and continuity 12:59
Workshop 8: Examples Class 4 26:49
Lecture 15: Sandwich theorem for real-valued function limits 47:27
Lecture 16: Application of the sandwich theorem 41:17
Lecture 17a: The boundedness theorem 24:20
Lecture 17b: Pointwise convergence: definition and examples. 10:38
Lecture 18: Sequences of functions 46:26
Lecture 19a: Uniform convergence 21:54
Lecture 19b: Rigorous Differential Calculus 21:36
Lecture 20: Fermat's Theorem, Rolle's Theorem and the Mean Value Theorem 51:51
Lecture 21: An introduction to Riemann integration 53:35

Mathematics - Foundations of Pure Mathematics - Joel Feinstein / U of Nottingham

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source: University of Nottingham     上次更新日期：2015年3月30日
These videos are also available for download on iTunes U at: https://itunes.apple.com/us/itunes-u/...
Dr Feinstein's blog may be viewed at: http://explainingmaths.wordpress.com
Dr Joel Feinstein is an Associate Professor in Pure Mathematics at the University of Nottingham.

Introduction to Foundations of Pure Mathematics 39:05
Sets and Numbers 42:23
Workshop 1: About this module 41:48
Definitions and Direct Proofs 47:34
Rational and irrational numbers 33:37
Workshop 2 26:13
More on rational and irrational numbers 47:05
Bezout's Lemma and Prime Factorization 48:52
Workshop 3 29:03
Sets and subsets 45:31
Cartesian Products and Relations 33:30
Workshop 4 34:40
Equivalence Relations and Equivalence Classes 45:27
Unions and Partitions41:46
Workshop 5 31:35
Equivalence Classes and Modular Arithmetic 50:10
Decimal expansions and rational numbers 49:28
Workshop 6 28:11
Functions and their graphs 40:54
Functions and sets 44:18
Workshop 726:21
Properties of functions 48:57
Finite sets and cardinality 42:46
Workshop 8 24:39
Permutations of finite sets 43:20
Permutations continued 41:50
Workshop 9 30:42
Cardinality for infinite sets 44:57
Conclusion of Cardinality for infinite sets 6:56
Countability and uncountability 47:47
Workshop 10 27:09
Discussions of Class Test 2 58:30

Mathematics - Functional Analysis--Joel Feinstein / U of Nottingham

# automatic playing for the 45 videos (click the up-left corner for the list)

source: University of Nottingham      上次更新日期：2014年6月28日
Functional analysis begins with a marriage of linear algebra and metric topology. These work together in a highly effective way to elucidate problems arising from differential equations. Solutions are sought in an infinite dimensional space of functions. This module paves the way by establishing the principal theorems (all due in part to the great Polish mathematician Stefan Banach) and exploring their diverse consequences.

Topics to be covered will include: -- norm topology and topological isomorphism; -- boundedness of operators; -- compactness and finite dimensionality; -- extension of functionals; -- weak*-compactness; -- sequence spaces and duality; -- basic properties of Banach algebras.

Dr Joel Feinstein is an Associate Professor in Pure Mathematics at the University of Nottingham. After reading mathematics at Cambridge, he carried out research for his doctorate at Leeds. He held a postdoctoral position in Leeds for one year, and then spent two years as a lecturer at Maynooth (Ireland) before taking up a permanent position at Nottingham. His main research interest is in functional analysis, especially commutative Banach algebras. Dr Feinstein has published two case studies on his use of IT in the teaching of mathematics to undergraduates. In 2009, Dr Feinstein was awarded a University of Nottingham Lord Dearing teaching award for his popular and successful innovations in this area.
Additional materials for this module are available at: http://unow.nottingham.ac.uk/resources/resource.aspx?hid=... and http://itunesu.nottingham.ac.uk/albums/64.rss. See also Dr Feinstein's blog at http://explainingmaths.wordpress.com/

Lecture 1:  35:10
Lecture 2: Complete metric spaces 41:30
Lecture 3: revision of Metric and Topological Spaces 44:33
Lecture 4: Complete metric spaces continued 45:13
Lecture 5a: Nowhere dense sets 32:31
Lecture 5b: Infinite products and Tychonoff's theorem 10:44
Lecture 6a: Discussion session on partially ordered sets and vector spaces 12:23
Lecture 6b: Continuation of discussion session on partially ordered sets 32:40
Lecture 7: Infinite products and Tychonoff's theorem 48:06
Lecture 8: The proof of Tychonoff's theorem 44:56
Lecture 9a: Infinite products and Tychonoff's theorem 26:15
Lecture 9b: Normed spaces and Banach spaces 12:54
Lecture 10: Normed spaces and Banach spaces 47:12
Lecture 11a:  26:41
Lecture 11b:  12:18
Lecture 12: Normed spaces and Banach spaces 43:20
Lecture 13a: Normed spaces and Banach spaces 9:02
Lecture 13b: Equivalence of norms 31:45
Lecture 14a: A recap of Equivalence of norms 3:49
Lecture 14b: A recap of Equivalence of norms 47:27
Lecture 15b: Linear Maps 35:05
Lecture 16a: Linear maps 24:43
Lecture 16b: Sequence spaces 17:45
Lecture 15a: Final discussion of Equivalence of norms 10:08
Lecture 17: Sequence spaces continued 46:31
Lecture 18a: more about Sequence spaces 36:01
Lecture 18b: Isomorphisms 7:08
Lecture 19a: Isomorphisms of normed spaces 24:50
Lecture 19b: Sums and Quotients of Vector Spaces 17:12
Lecture 20a - Sums and quotients of vector spaces - Conclusion of Section 3.6, printed slides 57-60 22:07
Lecture 20b - Section 3.7: Dual spaces - Section 3.7, printed slides 61-64 22:41
Lecture 21 - Duals and Double Duals - Section 3.7, printed slides 64-65 35:38
Lecture 22 - Conclusion of Section 3.7 and brief introduction to Section 3.8 41:20
Lecture 23 - Extensions of linear maps 45:54
Lecture 24 - Completions, quotients and Riesz's Lemma 40:45
Lecture 25 - The Weak-* Topology and the Banach-Alaoglu Theorem 42:58
Lecture 26 - Open Mappings and their Applications 38:30
Lecture 27 - Applications of the open mapping lemma 40:01
Lecture 28 - part a - Recap concerning convex sets which are symmetric about 0 2:04
Lecture 28 - part b - Chapter 5, printed slides 102-108, Proof of Open Mapping Theorem 44:29
Lecture 29 part a - Recap, and proof of the Closed Graph Theorem 18:15
Lecture 29 part b - The Uniform Boundedness Principle/Banach-Steinhaus 21:40
Lecture 30 - Commutative Banach Algebras, printed slides 1-19 47:33
Lecture 31 - Commutative Banach Algebras, printed slides 19-29 46:15
Lecture 32 - Discussion session on measure theory 46:16

Mathematics - Definitions, Proofs and Examples--Joel Feinstein / University of Nottingham

# automatic playing for the 18 videos (click the up-left corner for the list)

source: University of Nottingham      上次更新日期：2014年6月13日
These sessions are intended to reinforce material from lectures, while also providing more opportunities for students to hone their skills in a number of areas, including the following: working with formal definitions; making deductions from information given; writing relatively routine proofs; investigating the properties of examples; thinking up examples with specified combinations of properties. Dr Joel Feinstein is an Associate Professor in Pure Mathematics at the University of Nottingham. After reading mathematics at Cambridge, he carried out research for his doctorate at Leeds. He held a postdoctoral position in Leeds for one year, and then spent two years as a lecturer at Maynooth (Ireland) before taking up a permanent position at Nottingham. His main research interest is in functional analysis, especially commutative Banach algebras. Dr Feinstein's blog is available at http://explainingmaths.wordpress.com/

Target audience: suitable for anyone with a knowledge of elementary algebra and prime numbers, as may be obtained by studying A level mathematics.

Why do we do proofs? - Dr Joel Feinstein 30:33
How do we do proofs? Part I - Dr Joel Feinstein 28:54
How do we do proofs? Part II - Dr Joel Feinstein 25:58
Definitions, Proofs and Examples 1 36:27
Definitions, Proofs and Examples 2 28:48
Definitions, Proofs and Examples 3 29:12
Definitions, Proofs and Examples 4 26:03
Definitions, Proofs and Examples 5 31:19

Mathematics: Making the Invisible Visible 2012 (Keith Devlin / Stanford U)

# automatic playing for the 5 videos (click the up-left corner for the list)

source: Stanford      Last updated on 2014年9月25日
Often described as the science of patterns, mathematics is arguably humanity's most penetrating mental framework for uncovering the hidden patterns that lie behind everything we see, feel, and experience. Galileo described mathematics as the language in which the laws of the universe are written. Intended to give a broad overview of the field, these five illustrated lectures look at counting and arithmetic, shape and geometry, motion and calculus, and chance and probability, and end with a mind-stretching trip to infinity.

1. General Overview and the Development of Numbers 1:44:17
2. The Golden Ratio & Fibonacci Numbers: Fact versus Fiction 1:43:18
3. The Birth of Algebra 1:44:24
4. Calculus: One of the Most Successful Technologies 1:42:48
5. How Did Human Beings Acquire the Ability to do Math? 1:54:24