Math 523 Honors  Introd. to Modern Analysis

                                                           Course Id 48125   Spring 2025

                                                            Prof. Andrea R. Nahmod


Lectures :  Tuesdays and Thursdays  11:30am- 12:45pm  in  Hasbrouck 138

Book:    `Fundamental Ideas of Analysis'  by Michael C. Reed.  Publisher:  Wiley (ISBN: 0471159964) 

Syllabus:  We will work through the text, our goal being to cover the most important sections in Chapters 1–6. The course serves as a more rigorous and in depth  study of some topics seen in calculus (eg.  Sequences, The Riemann Integral, Differentiation, Sequence of functions,  Series of functions) and goes further into ideas and methods of analysis that play a fundamental role in differential equations, probability theory, numerical analysis, differential geometry, etc. 

Office Hours:  Wednesdays 2:30pm-3:30pm and by appointment  in  LGRT # 1588  (my office).
Email me any time with questions at     nahmod at umass dot edu

Special Announcements: (1) No class on Thursday February 20th since it is a `Monday schedule' (President's Day Holiday).

                                                 

Assignments:  Homework and special projects will be assigned as appropriate and collected regularly.
All assignments and their `due dates' will be posted on this web page by clicking in

       
                                                        HOMEWORK, etc.

--As a general rule no late homework will be accepted unless there are special circumstances and we've
made special arrangements beforehand.

--If you feel sick please do not attend class and contact me ASAP so I can help 
you keep up. You'll not lose your class participation or credit.

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Some Handouts do not open if not needed! Attempt by yourselves first:

Hints to Problem 12 section 1.1

Hints Problem 9 c) and d) section 1.3

Hints for some Problems in section 2.1

Hint Problem 5 (full) Section 2.2

Hints for section 2.2 and 2.4

Hints for Project I


Grading Policy.
  Your grade will be based on:


Some Important Remarks: 

* Due to the amount of material to be covered in this course the pace might be fast at times. And since later sections depend on ideas covered earlier, it is important not to fall behind.
* You are expected to read the sections ahead that we will be covering i class. We will not have time to cover all proofs and examples from the text, but you are still expected to read the whole section yourself and be familiar with it.  You are always welcome to discuss the material with me.  

* Please let me know in advance of any special circumstances which may prevent you from attending classes.

* Help each other out and discuss difficulties, but do your own work (!).
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Mandatory Information:

Accommodation Statement

The University of Massachusetts Amherst is committed to providing an equal educational opportunity for all students.  If you have a documented physical, psychological, or learning disability on file with Disability Services (DS), you may be eligible for reasonable academic accommodations to help you succeed in this course.  If you have a documented disability that requires an accommodation, please notify me within the first two weeks of the semester so that we may make appropriate arrangements.  For further information, please visit Disability Services (https://www.umass.edu/disability/)

Academic Honesty Statement

Since the integrity of the academic enterprise of any institution of higher education requires honesty in scholarship and research, academic honesty is required of all students at the University of Massachusetts Amherst.  Academic dishonesty is prohibited in all programs of the University.  Academic dishonesty includes but is not limited to: cheating, fabrication, plagiarism, and facilitating dishonesty.  Appropriate sanctions may be imposed on any student who has committed an act of academic dishonesty.  Instructors should take reasonable steps to address academic misconduct.  Any person who has reason to believe that a student has committed academic dishonesty should bring such information to the attention of the appropriate course instructor as soon as possible.  Instances of academic dishonesty not related to a specific course should be brought to the attention of the appropriate department Head or Chair.  Since students are expected to be familiar with this policy and the commonly accepted standards of academic integrity, ignorance of such standards is not normally sufficient evidence of lack of intent (http://www.umass.edu/dean_students/codeofconduct/acadhonesty/).

Title IX Statement –

In accordance with Title IX of the Education Amendments of 1972 that prohibits gender-based discrimination in educational settings that receive federal funds, the University of Massachusetts Amherst is committed to providing a safe learning environment for all students, free from all forms of discrimination, including sexual assault, sexual harassment, domestic violence, dating violence, stalking, and retaliation. This includes interactions in person or online through digital platforms and social media. Title IX also protects against discrimination on the basis of pregnancy, childbirth, false pregnancy, miscarriage, abortion, or related conditions, including recovery. There are resources here on campus to support you. A summary of the available Title IX resources (confidential and non-confidential) can be found at the following link: https://www.umass.edu/titleix/resources. You do not need to make a formal report to access them. If you need immediate support, you are not alone. Free and confidential support is available 24 hours a day / 7 days a week / 365 days a year at the SASA Hotline 413-545-0800.

 
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