Problems in mathematical analysis 1. Real numbers, sequences, series

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  • Problems in Mathematical Analysis I: Real Numbers, Sequences and Series resources
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  • A Problem Book in Real Analysis
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  • Possible upcoming homeworks
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    • Real Analysis I. Taped YouTube Lectures : These lectures were taped in , and although the lectures I give this year may not be identical, they will be close enough that you may find it valuable to use them for review. Or, better yet, watch them before the class lecture, and then during class you can ask questions! I do not encourage using these lectures as a substitute for class, however, since we will be doing slightly different things and interactions with me and other students will be critical for your learning.

    Real Analysis Lectures, Spring Due Thurs Jan Read this article by Carol Dweck and my handout on good mathematical writing. Fill out this survey. Then turn in brief answers to these questions.

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    Keep in mind the handout and the homework format as you write up your answers. From the article by Carol Dweck: 1. When faced with a mathematical challenge, describe 3 ways a person with a growth mindset would respond differently than a person with a fixed mindset. Directly from the handout on good writing: 2. What is a good rule of thumb for what you should assume of your audience as you write your homework sets?

    Do you see why the proof by contradiction on page 3 is not really a proof by contradiction? Name 3 things a lazy writer would do that a good writer wouldn't. What's the difference in meaning between these three phrases? There are many places in his proof where he could have used symbols to express his ideas, but he does not. What would you change about his presentation if you were writing for a high school audience? Give a specific example.

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    Your homework should be handed in three parts. Part A should have problems 1 and 2. Part B should have problems 3 and 4. Part C should have problems 5 and 6. Due Jan Problem B. Problem C. Show that the addition of rational numbers is well-defined. Problem D. Define a multiplication of rational numbers corresponding to the one you are used to , and show this multiplication is well-defined.

    For problems B, C, D, you may assume you know properties of integers, including the cancellation law of Z. You cannot assume that you know how to divide integers because that is really multiplication by a rational , nor how to add or multiply rationals because that is what you are trying to show! Do also Chapter 1 1, 2, 3a.

    Problems in Mathematical Analysis I: Real Numbers, Sequences and Series resources

    For these problems in Rudin, you may assume that you know familiar properties of rational numbers that we were proving in Lecture 2. Part A should have problems B and C. Search for books, journals or webpages All Pages Books Journals. View on ScienceDirect. Editors: L. Lyusternik A.

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    Introduction to Real Analysis(giuliettasprint.konfer.eu-II)

    Real Numbers and their Representation 1. Real Numbers 2. The Numerical Straight Line 3. Sets of Real Numbers 5. Bounded Sets, Upper and Lower Bounds 6. Sequences 1. Functions of One Variable 2.

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    Upper and Lower Bounds of a Function 3. Even and Odd Functions 4. Inverse Functions 5. Periodic Functions 6. Functional Equations 7. Numerical Sequences 8. Upper and Lower Bounds of a Sequence 9. Maximum Term of a Sequence Monotonic Sequences Passage to the Limit 1.

    The Limit Point of a Set 2. The Limit Point and Limit of a Sequence 3.

    A Problem Book in Real Analysis

    Fundamental Theorems Concerning Limits 4. Some Propositions on Limits 5. Upper and Lower Limits of a Sequence 6. Uniformly Distributed Sequences 7. Recurrent Sequences 8.

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    Surajit Saha marked it as to-read Feb 21, Part C should have problems 20 and S. Due Thurs Jan Power Series Both methods are described below.

    Limit of a Function Right and Left Continuity of a Function Continuous and Discontinuous Functions Functional Sequences Uniform Convergence of Functions Convergence in the Mean The Symbols o x and O x Monotonie Functions Scalar Product 4. A Linear System and its Basis 5.

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    We learn by doing. We learn mathematics by doing problems. This book is the first volume of a series of books of problems in mathematical. Problems in mathematical analysis. I. Real numbers, sequences and series / W. J . Kaczor, M. T. Nowak. p. cm. — (Student mathematical library, ISSN

    Linear Functions 6. Linear Envelope 7. Orthogonal Systems of Vectors 8. Biorthogonal Systems of Vectors 9. Passage to the Limit, Continuous Functions and Operators 1. Passage to the Limit in n-dimensional Space 2. Series of Vectors 3. Continuous Functions of n Variables 4. Periodic Functions of n Variables. Manifolds of Constancy 5.

    • Rewiring the Real: In Conversation with William Gaddis, Richard Powers, Mark Danielewski, and Don DeLillo (Religion, Culture, and Public Life).
    • Theophany: The Neoplatonic Philosophy of Dionysius the Areopagite.
    • Problems in Mathematical Analysis I: Real Numbers, Sequences and Series!
    • M2: Analysis I - Sequences and Series (2016-2017).
    • Problems in Mathematical Analysis I: Real Numbers, Sequences and Series page vi.
    • Possible upcoming homeworks!

    Passage to the Limit for Linear Envelopes 6. Operators From En into Em 7. Iterative Sequences 8. Convex Bodies in n-dimensional Space 1. Skip to main content. Mathematical Institute Course Management. You are here Home. Lecturer s :. Course Term:. Course Lecture Information:. Course Overview:.

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    Course Syllabus:. Course Synopsis:. Reading List:. Further Reading:.