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18.S34 Problem Solving Seminar (MIT) 18.S34 Problem Solving Seminar (MIT)

Description

This course,which is geared toward Freshmen, is an undergraduate seminar on mathematical problem solving. It is intended for students who enjoy solving challenging mathematical problems and who are interested in learning various techniques and background information useful for problem solving. Students in this course are expected to compete in a nationwide mathematics contest for undergraduates. This course,which is geared toward Freshmen, is an undergraduate seminar on mathematical problem solving. It is intended for students who enjoy solving challenging mathematical problems and who are interested in learning various techniques and background information useful for problem solving. Students in this course are expected to compete in a nationwide mathematics contest for undergraduates.

Subjects

Pigeonhole Principle | Pigeonhole Principle | probability | probability | congruences and divisibility | congruences and divisibility | recurrences | recurrences | limits | limits | greatest integer function | greatest integer function | inequalities | inequalities | Putnam practice | Putnam practice | hidden independence | hidden independence | roots of polynomials | roots of polynomials

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htm

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18.726 Algebraic Geometry (MIT) 18.726 Algebraic Geometry (MIT)

Description

This course provides an introduction to the language of schemes, properties of morphisms, and sheaf cohomology. Together with 18.725 Algebraic Geometry, students gain an understanding of the basic notions and techniques of modern algebraic geometry. This course provides an introduction to the language of schemes, properties of morphisms, and sheaf cohomology. Together with 18.725 Algebraic Geometry, students gain an understanding of the basic notions and techniques of modern algebraic geometry.

Subjects

category theory | category theory | sheaves | sheaves | abelian sheaves | abelian sheaves | shcemes | shcemes | morphisms | morphisms | projective morphisms | projective morphisms | differentials | differentials | divisors | divisors | homological algebra | homological algebra | algebraic geometry | algebraic geometry | cohomology | cohomology | quasicoherent sheaves | quasicoherent sheaves | projective spaces | projective spaces | hilbert polynomials | hilbert polynomials | gaga | gaga | serre duality | serre duality | cohen-macaulay schemes | cohen-macaulay schemes | riemann-roch | riemann-roch | etale cohomology | etale cohomology

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htm

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18.S34 Problem Solving Seminar (MIT) 18.S34 Problem Solving Seminar (MIT)

Description

This course, which is geared toward Freshmen, is an undergraduate seminar on mathematical problem solving. It is intended for students who enjoy solving challenging mathematical problems and who are interested in learning various techniques and background information useful for problem solving. Students in this course are expected to compete in a nationwide mathematics contest for undergraduates. This course, which is geared toward Freshmen, is an undergraduate seminar on mathematical problem solving. It is intended for students who enjoy solving challenging mathematical problems and who are interested in learning various techniques and background information useful for problem solving. Students in this course are expected to compete in a nationwide mathematics contest for undergraduates.

Subjects

Pigeonhole Principle | Pigeonhole Principle | probability | probability | congruences and divisibility | congruences and divisibility | recurrences | recurrences | limits | limits | greatest integer function | greatest integer function | inequalities | inequalities | Putnam practice | Putnam practice | hidden independence | hidden independence | roots of polynomials | roots of polynomials

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htm

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6.094 Introduction to MATLAB® (MIT) 6.094 Introduction to MATLAB® (MIT)

Description

This course provides an aggressively gentle introduction to MATLAB®. It is designed to give students fluency in MATLAB, including popular toolboxes. The course consists of interactive lectures with a computer running MATLAB for each student. Problem-based MATLAB assignments are given which require significant time on MATLAB. This course is offered during the Independent Activities Period (IAP), which is a special 4-week term at MIT that runs from the first week of January until the end of the month. This course provides an aggressively gentle introduction to MATLAB®. It is designed to give students fluency in MATLAB, including popular toolboxes. The course consists of interactive lectures with a computer running MATLAB for each student. Problem-based MATLAB assignments are given which require significant time on MATLAB. This course is offered during the Independent Activities Period (IAP), which is a special 4-week term at MIT that runs from the first week of January until the end of the month.

Subjects

matlab | matlab | simulink | simulink | matlab programming | matlab programming | variables | variables | plotting | plotting | scripts | scripts | functions | functions | flow control | flow control | linear algebra | linear algebra | polynomials | polynomials | optimization | optimization | differential equations | differential equations | ode | ode | probability | probability | statistics | statistics | data structures | data structures | images | images | animation | animation | debugging | debugging | symbolic math | symbolic math | toolboxes | toolboxes | scope | scope | function block | function block | nervous system | nervous system

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htm

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18.104 Seminar in Analysis: Applications to Number Theory (MIT) 18.104 Seminar in Analysis: Applications to Number Theory (MIT)

Description

18.104 is an undergraduate level seminar for mathematics majors. Students present and discuss subject matter taken from current journals or books. Instruction and practice in written and oral communication is provided. The topics vary from year to year. The topic for this term is Applications to Number Theory. 18.104 is an undergraduate level seminar for mathematics majors. Students present and discuss subject matter taken from current journals or books. Instruction and practice in written and oral communication is provided. The topics vary from year to year. The topic for this term is Applications to Number Theory.

Subjects

Infinitude of the primes | Infinitude of the primes | Summing powers of integers | Summing powers of integers | Bernoulli polynomials | Bernoulli polynomials | sine product formula | sine product formula | $\zeta(2n)$ | $\zeta(2n)$ | Fermat's Little Theorem | Fermat's Little Theorem | Fermat's Great Theorem | Fermat's Great Theorem | Averages of arithmetic functions | Averages of arithmetic functions | arithmetic-geometric mean | arithmetic-geometric mean | Gauss' theorem | Gauss' theorem | Wallis's formula | Wallis's formula | Stirling's formula | Stirling's formula | prime number theorem | prime number theorem | Riemann's hypothesis | Riemann's hypothesis | Euler's proof of infinitude of primes | Euler's proof of infinitude of primes | Density of prime numbers | Density of prime numbers | Euclidean algorithm | Euclidean algorithm | Golden Ratio | Golden Ratio

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htm

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18.996 Random Matrix Theory and Its Applications (MIT) 18.996 Random Matrix Theory and Its Applications (MIT)

Description

This course is an introduction to the basics of random matrix theory, motivated by engineering and scientific applications. This course is an introduction to the basics of random matrix theory, motivated by engineering and scientific applications.

Subjects

Random matrix theory | Random matrix theory | Matrix Jacobians | Matrix Jacobians | Wishart Matrices | Wishart Matrices | Wigner's Semi-Circular laws | Wigner's Semi-Circular laws | Matrix beta ensembles | Matrix beta ensembles | free probability | free probability | spherical coordinates | spherical coordinates | wedging | wedging | Plucker coordinates | Plucker coordinates | matrix factorizations | matrix factorizations | householder transformations | householder transformations | Stiefel manifold | Stiefel manifold | Cauchey-Binet theorem | Cauchey-Binet theorem | Telatar's paper | Telatar's paper | level densities | level densities | orthogonal polynomials | orthogonal polynomials | matrix integrals | matrix integrals | hypergeometric functions | hypergeometric functions | wireless communictions | wireless communictions | eigenvalue density | eigenvalue density | sample covariance matrices | sample covariance matrices | Marcenko-Pastur theorem | Marcenko-Pastur theorem | wireless communications | wireless communications

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htm

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18.S34 Problem Solving Seminar (MIT) 18.S34 Problem Solving Seminar (MIT)

Description

This course is an undergraduate seminar on mathematical problem solving. It is intended for students who enjoy solving challenging mathematical problems and who are interested in learning various techniques and background information useful for problem solving. This course is an undergraduate seminar on mathematical problem solving. It is intended for students who enjoy solving challenging mathematical problems and who are interested in learning various techniques and background information useful for problem solving.

Subjects

Pigeonhole Principle | Pigeonhole Principle | probability | probability | congruences and divisibility | congruences and divisibility | recurrences | recurrences | limits | limits | greatest integer function | greatest integer function | inequalities | inequalities | Putnam practice | Putnam practice | hidden independence | hidden independence | roots of polynomials | roots of polynomials

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htm

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18.726 Algebraic Geometry (MIT)

Description

This course provides an introduction to the language of schemes, properties of morphisms, and sheaf cohomology. Together with 18.725 Algebraic Geometry, students gain an understanding of the basic notions and techniques of modern algebraic geometry.

Subjects

category theory | sheaves | abelian sheaves | shcemes | morphisms | projective morphisms | differentials | divisors | homological algebra | algebraic geometry | cohomology | quasicoherent sheaves | projective spaces | hilbert polynomials | gaga | serre duality | cohen-macaulay schemes | riemann-roch | etale cohomology

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see https://ocw.mit.edu/terms/index.htm

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Beginning Algebra

Description

This course is intended to provide the student with a strong foundation for intermediate algebra and beyond. Beginning Algebra has been developed through a partnership with the Washington State Board for Community and Technical Colleges; the Saylor Foundation has modified some WSBCTC materials. This free course may be completed online at any time. See course site for detailed overview and learning outcomes. (Mathematics 001)

Subjects

algebra | exponents | polynomials | graphing | Computer science | I100

License

Attribution 2.0 UK: England & Wales Attribution 2.0 UK: England & Wales http://creativecommons.org/licenses/by/2.0/uk/ http://creativecommons.org/licenses/by/2.0/uk/

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18.S34 Problem Solving Seminar (MIT)

Description

This course, which is geared toward Freshmen, is an undergraduate seminar on mathematical problem solving. It is intended for students who enjoy solving challenging mathematical problems and who are interested in learning various techniques and background information useful for problem solving. Students in this course are expected to compete in a nationwide mathematics contest for undergraduates.

Subjects

Pigeonhole Principle | probability | congruences and divisibility | recurrences | limits | greatest integer function | inequalities | Putnam practice | hidden independence | roots of polynomials

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see https://ocw.mit.edu/terms/index.htm

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Numerical Analysis

Description

Numerical analysis is the study of the methods used to solve problems involving continuous variables. It is a highly applied branch of mathematics and computer science, wherein abstract ideas and theories become the quantities describing things we can actually touch and see. Suggested prerequisites for this course are MA211: Linear Algebra, MA221: Differential Equations, and either MA302/CS101: Introduction to Computer Science, or a background in some programming language. Programming ideas will be illustrated in pseudocode and implemented in the open-source high-level computing environment. This free course may be completed online at any time. See course site for detailed overview and learning outcomes. (Mathematics 213)

Subjects

computer arithmetic | polynomials | functions | differential equations | computer science | continuous variables | Computer science | I100

License

Attribution 2.0 UK: England & Wales Attribution 2.0 UK: England & Wales http://creativecommons.org/licenses/by/2.0/uk/ http://creativecommons.org/licenses/by/2.0/uk/

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Abstract Algebra II

Description

This course is a continuation of Abstract Algebra I: the student will revisit structures like groups, rings, and fields as well as mappings like homomorphisms and isomorphisms. The student will also take a look at ring factorization, general lattices, and vector spaces. Later this course presents more advanced topics, such as Galois theory—one of the most important theories in algebra, but one that requires a thorough understanding of much of the content we will study beforehand. This free course may be completed online at any time. See course site for detailed overview and learning outcomes. (Mathematics 232)

Subjects

groups | theorem | abstract algebra | polynomials | rings | vector spaces | linear | transformation | galois theory | Computer science | I100

License

Attribution 2.0 UK: England & Wales Attribution 2.0 UK: England & Wales http://creativecommons.org/licenses/by/2.0/uk/ http://creativecommons.org/licenses/by/2.0/uk/

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18.104 Seminar in Analysis: Applications to Number Theory (MIT)

Description

18.104 is an undergraduate level seminar for mathematics majors. Students present and discuss subject matter taken from current journals or books. Instruction and practice in written and oral communication is provided. The topics vary from year to year. The topic for this term is Applications to Number Theory.

Subjects

Infinitude of the primes | Summing powers of integers | Bernoulli polynomials | sine product formula | $\zeta(2n)$ | Fermat's Little Theorem | Fermat's Great Theorem | Averages of arithmetic functions | arithmetic-geometric mean | Gauss' theorem | Wallis's formula | Stirling's formula | prime number theorem | Riemann's hypothesis | Euler's proof of infinitude of primes | Density of prime numbers | Euclidean algorithm | Golden Ratio

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see https://ocw.mit.edu/terms/index.htm

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18.S34 Problem Solving Seminar (MIT)

Description

This course is an undergraduate seminar on mathematical problem solving. It is intended for students who enjoy solving challenging mathematical problems and who are interested in learning various techniques and background information useful for problem solving.

Subjects

Pigeonhole Principle | probability | congruences and divisibility | recurrences | limits | greatest integer function | inequalities | Putnam practice | hidden independence | roots of polynomials

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see https://ocw.mit.edu/terms/index.htm

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18.996 Random Matrix Theory and Its Applications (MIT)

Description

This course is an introduction to the basics of random matrix theory, motivated by engineering and scientific applications.

Subjects

Random matrix theory | Matrix Jacobians | Wishart Matrices | Wigner's Semi-Circular laws | Matrix beta ensembles | free probability | spherical coordinates | wedging | Plucker coordinates | matrix factorizations | householder transformations | Stiefel manifold | Cauchey-Binet theorem | Telatar's paper | level densities | orthogonal polynomials | matrix integrals | hypergeometric functions | wireless communictions | eigenvalue density | sample covariance matrices | Marcenko-Pastur theorem | wireless communications

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see https://ocw.mit.edu/terms/index.htm

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18.S34 Problem Solving Seminar (MIT)

Description

This course,which is geared toward Freshmen, is an undergraduate seminar on mathematical problem solving. It is intended for students who enjoy solving challenging mathematical problems and who are interested in learning various techniques and background information useful for problem solving. Students in this course are expected to compete in a nationwide mathematics contest for undergraduates.

Subjects

Pigeonhole Principle | probability | congruences and divisibility | recurrences | limits | greatest integer function | inequalities | Putnam practice | hidden independence | roots of polynomials

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see https://ocw.mit.edu/terms/index.htm

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(MIT)

Description

This course provides an aggressively gentle introduction to MATLAB®. It is designed to give students fluency in MATLAB, including popular toolboxes. The course consists of interactive lectures with a computer running MATLAB for each student. Problem-based MATLAB assignments are given which require significant time on MATLAB. This course is offered during the Independent Activities Period (IAP), which is a special 4-week term at MIT that runs from the first week of January until the end of the month.

Subjects

matlab | simulink | matlab programming | variables | plotting | scripts | functions | flow control | linear algebra | polynomials | optimization | differential equations | ode | probability | statistics | data structures | images | animation | debugging | symbolic math | toolboxes | scope | function block | nervous system

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see https://ocw.mit.edu/terms/index.htm

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