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18 094J: Teaching College-Level Science and Engineering
2.00 Credits
Massachusetts Institute of Technology
Participatory seminar focuses on the knowledge and skills necessary for teaching science and engineering in higher education. Topics include theories of adult learning; course development; promoting active learning, problemsolving, and critical thinking in students; communicating with a diverse student body; using educational technology to further learning; lecturing; creating effective tests and assignments; and assessment and evaluation. Students research and present a relevant topic of particular interest. Appropriate for both novices and those with teaching experience.
Prerequisite:
Prereq: None
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18 094J - Teaching College-Level Science and Engineering
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18 095: Mathematics Lecture Series
2.00 Credits
Massachusetts Institute of Technology
Ten lectures by mathematics faculty members on interesting topics from both classical and modern mathematics. All lectures accessible to students with calculus background and an interest in mathematics. At each lecture, reading and exercises are assigned. Students prepare these for discussion in a weekly problem session.
Prerequisite:
Prereq: Calculus I (GIR)
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18 095 - Mathematics Lecture Series
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18 098: Independent Study
0.00 - 6.00 Credits
Massachusetts Institute of Technology
Studies or special individual reading arranged in consultation with individual faculty members and subject to departmental approval.
Prerequisite:
Prereq: Permission of instructor
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18 098 - Independent Study
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18 099: Independent Study
0.00 - 6.00 Credits
Massachusetts Institute of Technology
Studies (during IAP) or special individual reading (during regular terms). Arranged in consultation with individual faculty members and subject to departmental approval.
Prerequisite:
Prereq: Permission of instructor
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18 099 - Independent Study
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18 100A: Real Analysis
3.00 Credits
Massachusetts Institute of Technology
Credit cannot also be received for 18.100B, 18.100C
Prerequisite:
Prereq: Calculus II (GIR); 18.03 or 18.034
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18 100A - Real Analysis
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18 100B: Real Analysis
3.00 Credits
Massachusetts Institute of Technology
Credit cannot also be received for 18.100A, 18.100C
Prerequisite:
Prereq: Calculus II (GIR); 18.03 or 18.034
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18 100B - Real Analysis
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18 100C: Real Analysis
4.00 Credits
Massachusetts Institute of Technology
Three options offered, each covering fundamentals of mathematical analysis: convergence of sequences and series, continuity, differentiability, Riemann integral, sequences and series of functions, uniformity, interchange of limit operations. Each option shows the utility of abstract concepts and teaches understanding and construction of proofs. Option A: Proofs and definitions are less abstract. Gives applications where possible. Concerned primarily with the real line. Option B: More demanding; for students with more mathematical maturity. Places more emphasis on point-set topology and n-space. Option C: 15-unit (4-0-11) variant of Option B, with further instruction and practice in written communication. Enrollment limited in Option C. Enrollment limited.
Prerequisite:
Prereq: Calculus II (GIR); 18.03 or 18.034
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18 100C - Real Analysis
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18 101: Analysis and Manifolds
3.00 Credits
Massachusetts Institute of Technology
Introduction to the theory of manifolds: vector fields and densities on manifolds, integral calculus in the manifold setting and the manifold version of the divergence theorem. 18.901 helpful but not required.
Prerequisite:
Prereq: 18.100; 18.06, 18.700, or 18.701
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18 101 - Analysis and Manifolds
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18 102: Introduction to Functional Analysis
3.00 Credits
Massachusetts Institute of Technology
Normed spaces, completeness, functionals, Hahn-Banach theorem, duality, operators. Lebesgue measure, measurable functions, integrability, completeness of L-p spaces. Hilbert space. Compact, Hilbert-Schmidt and trace class operators. Spectral theorem.
Prerequisite:
Prereq: 18.100; 18.06, 18.700, or 18.701
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18 102 - Introduction to Functional Analysis
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18 103: Fourier Analysis-Theory and Applications
3.00 Credits
Massachusetts Institute of Technology
Roughly half the subject devoted to the theory of the Lebesgue integral with applications to probability, and half to Fourier series and Fourier integrals.
Prerequisite:
Prereq: 18.100; 18.06, 18.700, or 18.701
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18 103 - Fourier Analysis-Theory and Applications
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