Math 4332 - Introduction to Real Analysis II -Ĭourse Description: Further development and applications of concepts from MATH 4331. It is assumed that the student is familiar with the material of Math 3333 (our first course in analysis), including an introduction to the real numbers, basic properties of continuous, differentiable and integrable functions on the real line, and an ability to do epsilon-delta proofs. * Note: This course provides a solid introduction to deeper properties of the real numbers, continuous functions, differentiability and integration needed for advanced study in mathematics, science and engineering. Grading: Please consult your instructor's syllabus regarding any and all grading guidelines. Rudin, Principles of Mathematical Analysis 3rd edition, ISBN-13: 978-0070542358 Donsig, Real Analysis with Real Applications. Carothers, Real analysis, Cambridge (has excellent problem sets) Students can review most of these topics on their own in the first weeks excessive overlap should be avoided): Possible Textbooks: (Note that several of these texts begin with chapters devoted to material from the prerequisite class MATH 3333 and Calculus III, or material from MATH 3334. See also the longer PDF syllabus linked on this site, and the topics list for MATH 4332 below. Some instructors may cover some other topics such as the proof of the inverse/implicit function theorem in n dimensions, or Lebesgue integration in place of Riemann-Stieltjes above. For example all instructors will cover, in addition to most of the topics above, rigorous series convergence tests, normed and inner product spaces, uniform convergence of functions including polynomial approximation and power series, Baire category, the Arzela-Ascoli theorem, etc. Topics may vary depending on instructor's choice, and which topics are covered in the second semester MATH 4332. Instructor's Description: The above is the description in the official university catalogue which is slightly outdated. Topics include: convergence of sequence, continuity and uniform continuity of functions, sequences and series of functions, differentiation, and Riemann-Stieltjes integration. Students should contact instructor for the updated information on current course syllabus, textbooks, and course content*** - MATH 4331 - Introduction to Real Analysis I -Ĭourse Description: Study of metric spaces and real-valued functions. MATH 4331 - Introduction to Real Analysis I & Math 4332 - Introduction to Real Analysis II
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