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Download Course. This course covers the fundamentals of mathematical analysis: convergence of sequences and series, continuity, differentiability, Riemann integral, sequences and series of functions, uniformity, and the interchange of limit operations. It shows the utility of abstract concepts through a study of real numbers, and teaches an ...
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It shows the utility of abstract concepts through a study of...
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The Uncountabality of the Real Numbers Assignment 3 due 7...
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CreateSpace Independent Publishing Platform, 2018. ISBN:...
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Lecture Videos - Real Analysis | Mathematics | MIT...
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Recitations - Real Analysis | Mathematics | MIT...
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Assignments and Exams - Real Analysis | Mathematics | MIT...
- 18.100A: Complete Lecture Notes
Lecture 12: The Ratio, Root, and Alternating Series Tests....
- Syllabus
MIT students may choose to take one of three versions of Real Analysis; this version offers three additional units of credit for instruction and practice in written and oral presentation. The three options for 18.100: * Option A (18.100A) chooses less abstract definitions and proofs, and gives applications where possible. * Option B (18.100B ...
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Lebl, Jiří. Basic Analysis I: Introduction to Real Analysis, Volume 1. CreateSpace Independent Publishing Platform, 2018. ISBN: 9781718862401. [JL] = Basic Analysis: Introduction to Real Analysis (Vol. 1) (PDF - 2.2MB)by Jiří Lebl, June 2021 (used with permission) This book is available as a free PDF download. You can purchase a paper copy by follo...
The lecture notes were prepared by Paige Dote under the guidance of Dr. Rodriguez. Dr. Rodriguez’s Fall 2020 lecture notes in one file: 1. Real Analysis (PDF) 2. Real Analysis (ZIP)LaTeX source files
Reading: [JL] Section 0.3 Lecture 1: Sets, Set Operations, and Mathematical Induction (PDF) Lecture 1: Sets, Set Operations, and Mathematical Induction (TEX) 1. Sets and their operations (union, intersection, complement, DeMorgan’s laws), 2. The well-ordering principle of the natural numbers, 3. The theorem of mathematical induction and application...
Reading: [JL] Sections 1.1 and 1.2 Lecture 3: Cantor’s Remarkable Theorem and the Rationals’ Lack of the Least Upper Bound Property (PDF) Lecture 3: Cantor’s Remarkable Theorem and the Rationals’ Lack of the Least Upper Bound Property (TEX) 1. Cantor’s theorem about the cardinality of the power set of a set, 2. Ordered sets and the least upper boun...
Reading: [JL] Sections 1.2, 1.3, 1.5, and 2.1 Lecture 5: The Archimedian Property, Density of the Rationals, and Absolute Value (PDF) Lecture 5: The Archimedian Property, Density of the Rationals, and Absolute Value (TEX) 1. The Archimedean property of the real numbers, 2. The density of the rational numbers, 3. Using sup/inf’s and the absolute val...
Reading: [JL] Sections 2.1 and 2.2 Lecture 7: Convergent Sequences of Real Numbers (PDF) Lecture 7: Convergent Sequences of Real Numbers (TEX) 1. Monotone sequences and when they have a limit, 2. Subsequences. Lecture 8: The Squeeze Theorem and Operations Involving Convergent Sequences (PDF) Lecture 8: The Squeeze Theorem and Operations Involving C...
Reading: [JL] Sections 2.2, 2.3, 2.4, and 2.5 Lecture 9: Limsup, Liminf, and the Bolzano-Weierstrass Theorem (PDF) Lecture 9: Limsup, Liminf, and the Bolzano-Weierstrass Theorem (TEX) 1. The limsup and liminf of a bounded sequence, 2. The Bolzano-Weierstrass Theorem. Lecture 10: The Completeness of the Real Numbers and Basic Properties of Infinite ...
Reading: [JL] Sections 2.5 and 2.6 Lecture 11: Absolute Convergence and the Comparison Test for Series (PDF) Lecture 11: Absolute Convergence and the Comparison Test for Series (TEX) 1. Absolute convergence, 2. The comparison test, 3. p-series. Lecture 12: The Ratio, Root, and Alternating Series Tests (PDF) Lecture 12: The Ratio, Root, and Alternat...
Reading: [JL] Section 3.1 Lecture 13: Limits of Functions (PDF) Lecture 13: Limits of Functions (TEX) 1. Cluster points, 2. Limits of functions, 3. The relationship between limits of functions and limits of sequences.
Reading: [JL] Sections 3.1 and 3.2 Lecture 14: Limits of Functions in Terms of Sequences and Continuity (PDF) Lecture 14: Limits of Functions in Terms of Sequences and Continuity (TEX) 1. The characterization of limits of functions in terms of limits of sequences and applications, 2. One-sided limits, 3. The definition of continuity. Lecture 15: Th...
Jul 11, 2022 · Instructor: Dr. Casey Rodriguez View the complete course: http://ocw.mit.edu/courses/18-100a-real-analysis-fall-2020/ This course covers the fundamentals of ...
MIT 18.100A Real Analysis, Fall 2020Instructor: Dr. Casey RodriguezView the complete course: http://ocw.mit.edu/courses/18-100a-real-analysis-fall-2020/YouTu...
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It shows the utility of abstract concepts and teaches an understanding and construction of proofs. MIT students may choose to take one of three versions of Real Analysis; this version offers three additional units of credit for instruction and practice in written and oral presentation. The three options for 18.100:
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Lecture 12: The Ratio, Root, and Alternating Series Tests. We continue our study of convergence tests. Theorem 1 (Ratio test) Suppose xn 6= 0for all n and jxn+1j. L = lim. n!1 jxnj. exists. Then, 1. if L < 1 then P xn converges absolutely.
