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18.100B Analysis I (MIT) 18.100B Analysis I (MIT)

Description

Analysis I covers fundamentals of mathematical analysis: metric spaces, convergence of sequences and series, continuity, differentiability, Riemann integral, sequences and series of functions, uniformity, interchange of limit operations. Analysis I covers fundamentals of mathematical analysis: metric spaces, convergence of sequences and series, continuity, differentiability, Riemann integral, sequences and series of functions, uniformity, interchange of limit operations.

Subjects

mathematical analysis | mathematical analysis | convergence of sequences | convergence of sequences | convergence of series | convergence of series | continuity | continuity | differentiability | differentiability | Riemann integral | Riemann integral | sequences and series of functions | sequences and series of functions | uniformity | uniformity | interchange of limit operations | interchange of limit operations | utility of abstract concepts | utility of abstract concepts | construction of proofs | construction of proofs | point-set topology | point-set topology | n-space | n-space

License

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18.100B Analysis I (MIT) 18.100B Analysis I (MIT)

Description

Analysis I covers fundamentals of mathematical analysis: convergence of sequences and series, continuity, differentiability, Riemann integral, sequences and series of functions, uniformity, interchange of limit operations. MIT students may choose to take one of the two versions of 18.100. Option A chooses less abstract definitions and proofs, and gives applications where possible. Option B is more demanding and for students with more mathematical maturity; it places more emphasis on point-set topology and n-space, whereas Option A is concerned primarily with the real line. Analysis I covers fundamentals of mathematical analysis: convergence of sequences and series, continuity, differentiability, Riemann integral, sequences and series of functions, uniformity, interchange of limit operations. MIT students may choose to take one of the two versions of 18.100. Option A chooses less abstract definitions and proofs, and gives applications where possible. Option B is more demanding and for students with more mathematical maturity; it places more emphasis on point-set topology and n-space, whereas Option A is concerned primarily with the real line.

Subjects

mathematical analysis | mathematical analysis | convergence of sequences | convergence of sequences | convergence of series | convergence of series | continuity | continuity | differentiability | differentiability | Reimann integral | Reimann integral | sequences and series of functions | sequences and series of functions | uniformity | uniformity | interchange of limit operations | interchange of limit operations | utility of abstract concepts | utility of abstract concepts | construction of proofs | construction of proofs | point-set topology | point-set topology | n-space | n-space | sequences of functions | sequences of functions | series of functions | series of functions | applications | applications | real variable | real variable | metric space | metric space | sets | sets | theorems | theorems | differentiate | differentiate | differentiable | differentiable | converge | converge | uniform | uniform | 18.100 | 18.100

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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18.100C Analysis I (MIT) 18.100C Analysis I (MIT)

Description

This course is meant as a first introduction to rigorous mathematics; understanding and writing of proofs will be emphasized. We will cover basic notions in real analysis: point-set topology, metric spaces, sequences and series, continuity, differentiability, and integration. This course is meant as a first introduction to rigorous mathematics; understanding and writing of proofs will be emphasized. We will cover basic notions in real analysis: point-set topology, metric spaces, sequences and series, continuity, differentiability, and integration.

Subjects

analysis | analysis | sequences | sequences | series | series | continuity | continuity | differentiability | differentiability | Riemann | Riemann | uniformity | uniformity | limit operations | limit operations | proofs | proofs | point-set topology | point-set topology | n-space | n-space | communication | communication | writing | writing

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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18.100A Analysis I (MIT) 18.100A Analysis I (MIT)

Description

Analysis I (18.100) in its various versions covers fundamentals of mathematical analysis: continuity, differentiability, some form of the Riemann integral, sequences and series of numbers and functions, uniform convergence with applications to interchange of limit operations, some point-set topology, including some work in Euclidean n-space. MIT students may choose to take one of three versions of 18.100: Option A (18.100A) chooses less abstract definitions and proofs, and gives applications where possible. Option B (18.100B) is more demanding and for students with more mathematical maturity; it places more emphasis from the beginning on point-set topology and n-space, whereas Option A is concerned primarily with analysis on the real line, saving for the last weeks work in 2-space (the pla Analysis I (18.100) in its various versions covers fundamentals of mathematical analysis: continuity, differentiability, some form of the Riemann integral, sequences and series of numbers and functions, uniform convergence with applications to interchange of limit operations, some point-set topology, including some work in Euclidean n-space. MIT students may choose to take one of three versions of 18.100: Option A (18.100A) chooses less abstract definitions and proofs, and gives applications where possible. Option B (18.100B) is more demanding and for students with more mathematical maturity; it places more emphasis from the beginning on point-set topology and n-space, whereas Option A is concerned primarily with analysis on the real line, saving for the last weeks work in 2-space (the pla

Subjects

mathematical analysis | mathematical analysis | convergence of sequences | convergence of sequences | convergence of series | convergence of series | continuity | continuity | differentiability | differentiability | Riemann integral | Riemann integral | sequences and series of functions | sequences and series of functions | uniformity | uniformity | interchange of limit operations | interchange of limit operations | utility of abstract concepts | utility of abstract concepts | construction of proofs | construction of proofs | point-set topology | point-set topology | n-space | n-space

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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18.100B Analysis I (MIT) 18.100B Analysis I (MIT)

Description

Analysis I covers fundamentals of mathematical analysis: convergence of sequences and series, continuity, differentiability, Riemann integral, sequences and series of functions, uniformity, and interchange of limit operations. Analysis I covers fundamentals of mathematical analysis: convergence of sequences and series, continuity, differentiability, Riemann integral, sequences and series of functions, uniformity, and interchange of limit operations.

Subjects

mathematical analysis | mathematical analysis | convergence of sequences | convergence of sequences | convergence of series | convergence of series | continuity | continuity | differentiability | differentiability | Riemann integral | Riemann integral | sequences and series of functions | sequences and series of functions | uniformity | uniformity | interchange of limit operations | interchange of limit operations | utility of abstract concepts | utility of abstract concepts | construction of proofs | construction of proofs | point-set topology | point-set topology | n-space | n-space

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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18.100B Analysis I (MIT)

Description

Analysis I covers fundamentals of mathematical analysis: convergence of sequences and series, continuity, differentiability, Riemann integral, sequences and series of functions, uniformity, and interchange of limit operations.

Subjects

mathematical analysis | convergence of sequences | convergence of series | continuity | differentiability | Riemann integral | sequences and series of functions | uniformity | interchange of limit operations | utility of abstract concepts | construction of proofs | point-set topology | n-space

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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18.100B Analysis I (MIT)

Description

Analysis I covers fundamentals of mathematical analysis: metric spaces, convergence of sequences and series, continuity, differentiability, Riemann integral, sequences and series of functions, uniformity, interchange of limit operations.

Subjects

mathematical analysis | convergence of sequences | convergence of series | continuity | differentiability | Riemann integral | sequences and series of functions | uniformity | interchange of limit operations | utility of abstract concepts | construction of proofs | point-set topology | n-space

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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18.100B Analysis I (MIT)

Description

Analysis I covers fundamentals of mathematical analysis: convergence of sequences and series, continuity, differentiability, Riemann integral, sequences and series of functions, uniformity, interchange of limit operations. MIT students may choose to take one of the two versions of 18.100. Option A chooses less abstract definitions and proofs, and gives applications where possible. Option B is more demanding and for students with more mathematical maturity; it places more emphasis on point-set topology and n-space, whereas Option A is concerned primarily with the real line.

Subjects

mathematical analysis | convergence of sequences | convergence of series | continuity | differentiability | Reimann integral | sequences and series of functions | uniformity | interchange of limit operations | utility of abstract concepts | construction of proofs | point-set topology | n-space | sequences of functions | series of functions | applications | real variable | metric space | sets | theorems | differentiate | differentiable | converge | uniform | 18.100

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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18.100C Analysis I (MIT)

Description

This course is meant as a first introduction to rigorous mathematics; understanding and writing of proofs will be emphasized. We will cover basic notions in real analysis: point-set topology, metric spaces, sequences and series, continuity, differentiability, and integration.

Subjects

analysis | sequences | series | continuity | differentiability | Riemann | uniformity | limit operations | proofs | point-set topology | n-space | communication | writing

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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18.100A Analysis I (MIT)

Description

Analysis I (18.100) in its various versions covers fundamentals of mathematical analysis: continuity, differentiability, some form of the Riemann integral, sequences and series of numbers and functions, uniform convergence with applications to interchange of limit operations, some point-set topology, including some work in Euclidean n-space. MIT students may choose to take one of three versions of 18.100: Option A (18.100A) chooses less abstract definitions and proofs, and gives applications where possible. Option B (18.100B) is more demanding and for students with more mathematical maturity; it places more emphasis from the beginning on point-set topology and n-space, whereas Option A is concerned primarily with analysis on the real line, saving for the last weeks work in 2-space (the pla

Subjects

mathematical analysis | convergence of sequences | convergence of series | continuity | differentiability | Riemann integral | sequences and series of functions | uniformity | interchange of limit operations | utility of abstract concepts | construction of proofs | point-set topology | n-space

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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