Math 1010 “Analysis: Functions of One Variable” (Spring 2011)

 

 

 

Lecture

 

 

Instructor: Armen Vagharshakyan

E-mail: armen[at]math[dot]brown[dot]edu

Lecture meeting time: MWF 2pm - 2:50pm
Lecture location: Watson (CIT) Center 219

 

Office hours: T 3:30-4:30pm, F 12:30pm-1:30pm

My office is: Kassar House, Room 219

       

 

 

General Course Information                                               

 

 

Textbook

 

We will mostly rely on online lecture notes and the book of Trench uploaded down there.

 

 

Course description in short

 

The official departmental syllabus can be found at: Math 1010. We cover the elementary Math. Logic, naive Set Theory (up to the axiom of choice), introduce real numbers rigorously (up to existence of roots), cover continuity (up to Peano curves), differentiability, Riemann integral (incl. improper and Riemann-Stieltjes integrals), numerical series, power series (incl. Taylor series), functional series in C[0,1] (up to Arzela-Ascoli) and convex functions.

 

 

Grading Policy

 

Best 10 out of 12 homework - 20%.

First midterm - 20%.

Second midterm - 25%.

Final exam - 35%.

 

Passing: those who score more than 50% will pass the class, some others might also pass the class.

 

Grade: at least 30% (of those registered for a letter grade) will get ‘A’. At most 25% (of those registered for a letter grade) will get ‘C’.

 

 

 

Assignments (in compliance with the DETAILED CLASS/HOMEWORK SCHEDULE)

 

 

Homework

 

 

Notes

 

Exams

 

HW 1: Problems, Solutions (average 28/30)

 

HW 2: Problems, Solutions (average 23/30)

 

HW 3: Problems, Solutions (average 25/30)

 

HW 4: Problems, Solutions (average 23/30)

 

HW 5: Problems, Solutions (average 24/30)

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HW 6: Problems, Solutions (average 28/30)

 

HW 7: Problems, Solutions (average 28/30)

 

HW 8: Problems, Solutions (average 27/30)

 

HW 9: Problems, Solutions (average 27/30)

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HW10: Problems, Solutions (average 28/30)

 

HW11: Problems, Solutions (average 28/30)

 

HW12: Problems, Solutions (average 28/30)

 

 

1. Lecture Notes (Elementary Math Logic and Real Numbers)

  

2. Real Analysis textbook

 

3. Convergence Tests: Kummer’s Test, Abel’s Test, Dirichlet’s Test

 

4. Opinion Survey

 

5[additional topic]. Arzela-Ascoli (in a bit more abstract setting than I prove in class)

 

6[additional topic]. Some stuff on Polynomial approximations

 

7[additional topic]. A proof of Weierstrass theorem (a bit more involved than I prove in class)

 

 

 

Midterm 1

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Midterm 2

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Final Exam