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- Lecture notes on algebraic curves are provided, covering projective spaces, plane curves, intersections of curves, the genus of a curve and the Riemann-Roch Theorem. The notes were prepared to accompany a course given by Balazs Szendroi at the Mathematical Institute, University of Oxford, England.
- Author
- Nigel Hitchin
- Publisher
- Mathematical Institute, University of Oxford
- http://www.maths.ox.ac.uk/system/files/coursematerial/2013/2378/8/13notes.pdf
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- Lecture notes on algebraic geometry are provided, covering affine algebraic varieties, projective varieties, examples, Hilbert's Nullstellensatz, primary decomposition, algebraic groups and group actions, discrete invariants, quasi-projective varieties, regular functions, tangent spaces and smooth points, rational maps and birational equivalence, and resolution of singularities. The notes were prepared to accompany a course given by Dr Gergely Berczi at the Mathematical Institute, University of Oxford, England.
- Author
- Elizabeth Baldwin; Gergely Berczi
- Publisher
- Mathematical Institute, University of Oxford
- http://www.maths.ox.ac.uk/system/files/coursematerial/2013/2651/34/notes.pdf
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- This resource provides the answers to the exercises included in the 21 chapters dealing with pure mathematics which are contained within the wider collection of A-Level course material provided by the Centre for Innovation in Mathematics Teaching, University of Plymouth. The individual chapters are also catalogued in the e-library.
- Publisher
- Centre for Innovation in Mathematics Teaching (CIMT), University of Plymouth
- http://www.cimt.plymouth.ac.uk/projects/mepres/alevel/pure_solutions.pdf
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- This resource introduces a range of concepts in Cartesian geometry, such as Cartesian and parametric curve equations, rectangular hyperbolae, and applying the general equation of a circle. Numerous worked examples are presented, with illustrations where applicable. The resource is chapter 17 of 21 dealing with pure mathematics, as part of a wider collection of A-Level course material provided by the Centre for Innovation in Mathematics Teaching, University of Plymouth. Answers to the exercises are also catalogued in the e-library.
- Publisher
- Centre for Innovation in Mathematics Teaching (CIMT), University of Plymouth
- http://www.cimt.plymouth.ac.uk/projects/mepres/alevel/pure_ch17.pdf
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- This resource provides a diagram and equations which represent cylindrical polar coordinates. The resource forms 1 of 13 advanced maths for engineers fact sheets produced by mathcentre.
- Publisher
- mathcentre
- http://www.mathcentre.ac.uk/search/?q=%22large+print%22&saudience=all&cat%5B%5D=512
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- This course describes motion along a line and different ways to represent this motion, through the use of graphs, equations and differential calculus. A range of applications and problem solving techniques are included. This intermediate module is provided by the UK Open University as part of its LearningSpace, a collection of over 800 free online courses (as at July 2016). It is expected to take 15 hours to complete.
- Publisher
- Open University
- http://www.open.edu/openlearn/science-maths-technology/science/physics-and-astronomy/describing-motion-along-line/content-section-0
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- This resource describes a range of more advanced features of trigonometry, and requires a basic level of knowledge. Topics covered include the six trigonometric functions, using identities, solving trigonometric equations, and applying the sine and cosine rules. Numerous worked examples are presented, with illustrations where applicable. The resource is chapter 15 of 21 dealing with pure mathematics, as part of a wider collection of A-Level course material provided by the Centre for Innovation in Mathematics Teaching, University of Plymouth. Answers to the exercises are also catalogued in the e-library.
- Publisher
- Centre for Innovation in Mathematics Teaching (CIMT), University of Plymouth
- http://www.cimt.plymouth.ac.uk/projects/mepres/alevel/pure_ch15.pdf
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- Lecture notes on geometric group theory are provided, covering free groups, presentations, group actions on trees, graphs of groups and groups as geometric objects. The notes were prepared to accompany a course given by Panos Papazoglou at the Mathematical Institute, University of Oxford, England.
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- Panos Papazoglou
- Publisher
- Mathematical Institute, University of Oxford
- http://www.maths.ox.ac.uk/system/files/coursematerial/2013/2409/40/Geometric_Group_Theory.pdf
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- Lecture notes are provided on complex manifolds, holomorphic functions and holomorphic maps, projective complex manifolds, almost complex structures, the Nijenhuis tensor, complex sub-manifolds and symplectic manifolds. The notes form lectures 1 and 2 of a course of 16 lectures given by Dominic Joyce at the Mathematical Institute, University of Oxford, England.
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- Dominic Joyce
- Publisher
- Mathematical Institute, University of Oxford
- http://www.maths.ox.ac.uk/system/files/coursematerial/2012/2694/3/KGlect12.pdf
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- Lecture notes are provided on curvature of Kahler manifolds, Riemann curvature of Riemannian manifolds, Riemannian curvature of Kahler metrics, the decomposition of tensors on complex manifolds, type decomposition of Riemann curvature of Kahler metrics, the Ricci form, Ricci flat Kahler manifolds and Calabi-Yau manifolds, Kahler-Einstein metrics, the Calabi conjecture, the existence of Calabi-Yau metrics, Ricci flatness and fundamental groups, the Weitzenbock formulae and the Bochner argument. The notes form lectures 11 and 12 of a course of 16 lectures given by Dominic Joyce at the Mathematical Institute, University of Oxford, England.
- Author
- Dominic Joyce
- Publisher
- Mathematical Institute, University of Oxford
- http://www.maths.ox.ac.uk/system/files/coursematerial/2012/2694/8/KGlect1112.pdf
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- Lecture notes are provided on Riemannian holonomy groups, parallel transport, reducible metrics, symmetric spaces, Berger's classification, Berger's tests, Berger's lists, principle bundles and G-structures, G-structures and holonomy groups, the Kahler holonomy groups, Kahler geometry from the point of view of Riemannian holonomy, Calabi-Yau manifolds, hyperkahler manifolds, Calabi-Yau 2-folds and Calabi-Yau geometry. The notes form lectures 13 and 14 of a course of 16 lectures given by Dominic Joyce at the Mathematical Institute, University of Oxford, England.
- Author
- Dominic Joyce
- Publisher
- Mathematical Institute, University of Oxford
- http://www.maths.ox.ac.uk/system/files/coursematerial/2012/2694/9/KGlect1314.pdf
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- Description
- Lecture notes are provided on moduli spaces in differential geometry, moduli spaces in algebraic geometry, deformations of compact complex manifolds, infinitesimal deformations, obstructions, moduli spaces of Riemann surfaces, moduli of del Pezzo surfaces, moduli of Calabi-Yau manifolds and period maps. The notes form lectures 15 and 16 of a course of 16 lectures given by Dominic Joyce at the Mathematical Institute, University of Oxford, England.
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- Dominic Joyce
- Publisher
- Mathematical Institute, University of Oxford
- http://www.maths.ox.ac.uk/system/files/coursematerial/2012/2694/10/KGlect1516.pdf
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- Lecture notes are provided on exterior forms on real manifolds, exterior forms on complex manifolds, (p,q)-forms in complex coordinates, holomorphic forms, canonical bundles, exterior forms on almost complex manifolds, (p,q)-forms in terms of representation theory, Kahler metrics, Hermitian metrics, the Kahler class and Kahler potentials, complex sub-manifolds, the Fubini-Study metric on CPn, exterior forms on Kahler manifolds, and operators on forms. The notes form lectures 3 and 4 of a course of 16 lectures given by Dominic Joyce at the Mathematical Institute, University of Oxford, England.
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- Dominic Joyce
- Publisher
- Mathematical Institute, University of Oxford
- http://www.maths.ox.ac.uk/system/files/coursematerial/2012/2694/4/KGlect34.pdf
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- Description
- Lecture notes are provided on the Hodge theory for compact Riemannian manifolds, the Hodge theory for Kahler manifolds, complex manifolds with no Kahler metrics, the Kahler cone, Lefschetz operators, the Hard Lefschetz Theorem, the Hodge conjecture, vector bundles on real manifolds, holomorphic vector bundles, Chern classes and holomorphic line bundles. The notes form lectures 5 and 6 of a course of 16 lectures given by Dominic Joyce at the Mathematical Institute, University of Oxford, England.
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- Dominic Joyce
- Publisher
- Mathematical Institute, University of Oxford
- http://www.maths.ox.ac.uk/system/files/coursematerial/2012/2694/5/KGlect56.pdf
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- Lecture notes are provided on line bundles and divisors, Picard groups, holomorphic sections, meromorphic sections, the cohomology of holomorphic vector bundles, Dolbeault-type cohomology for vector bundles, the Hirzebruch-Riemann-Roch (H-R-R) Theorem, Serre duality, and the Grothendieck Lemma. The notes form lectures 7 and 8 of a course of 16 lectures given by Dominic Joyce at the Mathematical Institute, University of Oxford, England.
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- Dominic Joyce
- Publisher
- Mathematical Institute, University of Oxford
- http://www.maths.ox.ac.uk/system/files/coursematerial/2012/2694/6/KGlect78.pdf
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- Lecture notes are provided on vanishing theorems, positive line bundles, the Kodaira Vanishing Theorem, the Serre Vanishing Theorem, applications to line bundles and divisors, the base locus and morphisms to projective spaces, the Kodaira Embedding Theorem, consequences of Kodaira embedding, finite covers, the Lefschetz Hyperplane Theorem, the adjunction formula and blow-ups. The notes form lectures 9 and 10 of a course of 16 lectures given by Dominic Joyce at the Mathematical Institute, University of Oxford, England.
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- Dominic Joyce
- Publisher
- Mathematical Institute, University of Oxford
- http://www.maths.ox.ac.uk/system/files/coursematerial/2012/2694/7/KGlect910.pdf
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- Description
- This book provides an introduction to Riemannian geometry and its principal physical application, Einsteins theory of general relativity. It assumes a background in linear algebra and advanced calculus. Chapters cover: the principal curvatures; the rules of calculus; Levi-Civita connections; the bundle of frames; connections on principle bundles; Gauss's lemma; special relativity; Hilbert's 1915 paper; submersions; Petrov types; and, the star operator. The book was written by Shlomo Sternberg from the Department of Mathematics, Harvard University, USA.
- Author
- Shlomo Sternberg
- Publisher
- Department of Mathematics, Harvard University
- http://www.math.harvard.edu/~shlomo/docs/semi_riemannian_geometry.pdf
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- Title
- Description
- This resource provides a diagram and equations which represent spherical polar coordinates. The resource forms 1 of 13 advanced maths for engineers fact sheets produced by mathcentre.
- Publisher
- mathcentre
- http://www.mathcentre.ac.uk/search/?q=%22large+print%22&saudience=all&cat%5B%5D=512
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- Title
- Description
- This course aims to teach concepts in surfaces, such as homeomorphism, orientability, the Euler characteristic and the classification theorem of compact surfaces. A wide range of examples and problems are included. This advance module is provided by the UK Open University as part of its LearningSpace, a collection of over 800 free online courses (as at July 2016). It is expected to take 20 hours to complete.
- Publisher
- Open University
- http://www.open.edu/openlearn/science-maths-technology/mathematics-and-statistics/mathematics/surfaces/content-section-0
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- These lecture notes examine the interrelationship between topology and group theory. They cover constructing spaces, homotopy, fundamental groups, free groups, group presentations and covering spaces. The notes were prepared to accompany a course given by Marc Lackenby at the Mathematical Institute, University of Oxford.
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- Marc Lackenby
- Publisher
- Mathematical Institute, University of Oxford
- https://www.maths.ox.ac.uk/system/files/coursematerial/2013/2376/12/tg230911.pdf
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- Description
- This resource describes the sine and cosine rules, and provides graphs of simple and inverse trigonometric functions. The resource forms 1 of 11 general maths fact sheets produced by mathcentre.
- Publisher
- mathcentre
- http://www.mathcentre.ac.uk/search/?q=%22large+print%22&saudience=all&cat%5B%5D=512
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- Description
- This resource on trigonometric functions (sines, cosines, tangents) includes quizzes, exercises and worked examples. It is one of a collection of mathematics support materials provided for schools and colleges by the University of Plymouth School of Mathematics and Statistics.
- Author
- Robin Horan; Martin Lavelle
- Publisher
- School of Mathematics and Statistics, University of Plymouth
- http://www.tech.plym.ac.uk/maths/resources/PDFLaTeX/trig1.pdf
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- Title
- Description
- This resource introduces a range of trigonometric concepts, such as sine, cosine and tangent. Topics covered include using radians to measure angles, unit conversion, formulating arc length and sector area, and solving equations using trigonometry. Numerous worked examples are presented, with illustrations where applicable. The resource is chapter 10 of 21 dealing with pure mathematics, as part of a wider collection of A-Level course material provided by the Centre for Innovation in Mathematics Teaching, University of Plymouth. Answers to the exercises are also catalogued in the e-library.
- Publisher
- Centre for Innovation in Mathematics Teaching (CIMT), University of Plymouth
- http://www.cimt.plymouth.ac.uk/projects/mepres/alevel/pure_ch10.pdf
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- Description
- This resource provides an introduction to some complex trigonometric concepts such as linear combinations, linear trigonometric equations, inverse functions, and higher integrations. Numerous worked examples are presented, with illustrations where applicable. The resource is chapter 1 of 9 dealing with further pure mathematics, as part of a wider collection of A-Level course material provided by the Centre for Innovation in Mathematics Teaching, University of Plymouth. Answers to the exercises are also catalogued in the e-library.
- Publisher
- Centre for Innovation in Mathematics Teaching (CIMT), University of Plymouth
- http://www.cimt.plymouth.ac.uk/projects/mepres/alevel/fpure_ch1.pdf
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- Title
- Description
- A reference sheet of various trigonometric functions and identities, such as trig ratios for an acute angle, standard triangles, definitions of common identities, and degrees and radians. The resource forms 1 of 11 general maths fact sheets produced by mathcentre.
- Publisher
- mathcentre
- http://www.mathcentre.ac.uk/search/?q=%22large+print%22&saudience=all&cat%5B%5D=512
