MATH 255: Honors Analysis 2

Winter 2022


Course web page: http://www.math.mcgill.ca/jakobson/courses/math255.html

Lectures:
  • Tuesday, Thursday, 10:00-11:30, tentatively in Leacock 26. The first week lectures will be on zoom, later location TBA.
  • The lectures will start on Thursday, January 6.
  • The lectures are scheduled to end on Tuesday, April 12.
  • Office hours to be announced.
    • Instructor: D. Jakobson
    Office: BH1220
    Tel: 398-3828
    E-mail: dmitry.jakobson AT mcgill.ca
    Web Page: www.math.mcgill.ca/jakobson
    Marker
  • to be announced
    • Description of BSc-MSc program
    Prerequisites: Math 254 or equivalent
    Texts:
  • Introduction to Real Analysis, by R. Bartle and D. Sherbert.
  • Supplementary: Principles of Mathematical Analysis, by W. Rudin.
  • Supplementary: Notes on Introductory Point-Set Topology by Allen Hatcher.
    • Syllabus: Basic point-set topology, metric spaces: open and closed sets, normed and Banach spaces, Holder and Minkowski inequalities, sequential compactness, Heine-Borel, Banach Fixed Point theorem. Riemann-(Stieltjes) integral, Fundamental Theorem of Calculus, Taylor's theorem. Uniform convergence. Infinite series, convergence tests, power series. Elementary functions.
    Math 255, Winter 2002
    Assignments: There will be be several assignments. Due dates will be announced on mycourses and on the course web page. There will be penalty for late assignments, except in cases of emergency. Depending on availability of markers and other factors, some problems may not be marked. Some assignments will be distributed through Crowdmark, the link will be on mycourses.

    Midterm:
  • There will be a crowdmark (timed) or a take-home midterm. Both midterms would be marked. You can attempt both tests, your mark will be the highest of the 2 marks that you receive.
  • The take-home midterm will be distributed before the study break, and will be due shortly after the end of the break.
  • The time window for the crowdmark midterm will be announced on Mycourses.
    • Final exam/assignment:
  • Details to be announced.
  • SUMS website should have arxived exams.
  • Supplemental: There will be a supplemental exam, counting 100% of the supplemental grade. No additional work will be accepted for D, F, or J.
    • Grading
  • Your final mark will be the largest of the following: (A) 25% Assignments + 25% Midterm + 50% Final assignment; OR (B) 30% Assignments + 70% Final assignment.
    • MyCourses: Your scores on assignments, midterm, final, and your final mark will be posted on MyCourses
    Course material from previous courses at McGill:
  • Prof. W. Labute. Math 255, 2003
  • Prof. V. Jaksic: 2011 Math 255
  • Prof. S. Drury's lecture notes:
    • Web links in Geometry and Topology
  • Lecture notes by Allen Hatcher
  • Lecture notes in general topology by Jan Derezinski
  • Glossary (wikipedia)
  • Another glossary
  • Rough guide to point-set topology
  • A wikibooks course in topology
  • A small handout of topological terms, prepared by P. Rosenthal
  • Introduction to Hausdorff distance: paper by J. Henrikson; page at Wapedia; applications to image recognition: Hausdorff distance between convex polygons, N. Gregoire and M. Bouillot.
    • Web links in Analysis
  • Metric space, Topology glossary, Functional analysis in Wikipedia
  • Norm, Holder's inequality, Minkowski inequality, Lp space, Hilbert space, Banach space, Cantor set, p-adic numbers in Wikipedia
  • Notes on differentiation of functions of several variables, implicit function theorem
  • Companion notes to Rudin's book
  • Yahoo group in Harmonic Analysis + a page with listings of conferences, successors to Terry Tao's old page on Harmonic analysis.
  • Terry Tao's blog
    • HELPDESK and their email: helpdesk@math.mcgill.ca
    WEB LINKS in Calculus, Algebra, Geometry and Differential Equations.
    HELPDESK and their email: helpdesk@math.mcgill.ca
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    NOTICE: McGill University values academic integrity. Therefore, all students must understand the meaning and consequences of cheating, plagiarism and other academic offences under the Code of Student Conduct and Disciplinary Procedures (see McGill web page on Academic Integrity for more information).
    NOTICE: In accord with McGill University's Charter of Student Rights, students in this course have the right to submit in English or in French any work that is to be graded.
    NOTICE: In the event of extraordinary circumstances beyond the University's control, the content and/or evaluation scheme in this course is subject to change, provided that there be timely communications to the students regarding the change.