MATH 310
Math 310, Sec 01, Elementary Real Analysis, Fall 2024
Prelims:
Assignments:
- Due 11/18. Read Ch 24 and do problems 24.2, 24.6, 24.11, 24.17.
- Due 11/13. Read Ch 23 and do problems 23.1 a,d,e,g 23.6, 23.7, 23.8, 23.9.
- Due 11/11. Read section 23. In section 19, do problems 19.1 a,c, and 19.5a,c (these should be ``one-line solutions'' using the statements in theorems
19.2 and 19.5). (More info: We are skipping sections 20-22).
- Due 11/4. Read Ch. 19 and do problems 19.1e, 19.2a,b,c, and 19.5e.
Also, prove this: an unbounded continuous function on an open interval (a,b) can never be extended to a continuous function on the closed interval [a,b], no
matter how one defines f(a) and f(b). We care about this because, by theorem
19.5 [which we'll do in class next], we can deduce that an unbounded continuous function on the open interval (a,b) is never uniformly continuous.
- Due 10/30. Read Ch. 18 and do problems 18.3, 18.4 (hint: distance
from x0), 18.7, 18.8, 18.9 (For the last three, use the statement of the
intermediate value theorem.)
- Due 10/28. Read Ch 17, and do problems 17.3 any 2 parts, 17.4, 17.5, 17.6,
17.7, 17.9a. (Problems 17.13 and 17.14 are fascinating).
- Due 10/23. Read Ch. 15 and do problems 15.1, 15.4 a,d, 15.6.
- Due 10/21. Do problems 14.1 (a,c,d,f), 14.3 (a,c,f), 14.5, 14.7, 14.14.
- Due 10/16. Read 14. (You might like problems 13.9, 13.10.)
- Due 10/15. Read 13 and do problems 13.1, 13.2, 13.3.
- Due 10/9. Do problems 12.1, 12.2, 12.7, 12.10 (all of these can be done
using the material we've covered so far; section 12 is not required). Is
there a sequence whose set of subsequential limits is precisely the set of
fractions 1/n, for n in the natural numbers? Read Section 13, at your
liesure. (We are not covering section 12, although the statement of Theorem 12.2 will be refereed to later in the course.)
- Due 10/7. Read Ch. 11 and do problems 11.2, 11.3, 11.4, 11.5, 11.10.
- Due 9/25. There are a lot of new concepts in Ch. 10. Be sure you know the
definitions well. Do problem 10.3 and use this to show that "the decimal
expansion of a number converges". Do problem 10.4, 10.5, 10.6.
- Due 9/23. Do problem 9.12, read section 10, and do problems 10.7, 10.9,
10.10. Do problem 11.2 c,d,e only (which uses only section 10).
- Due 9/18. Read section 10 (to p. 60) and do problems 10.1, 10.4
(only part about Theorem 10.2). Do problems 9.8 a,b,c, 9.9 a, 9.10b, 9.13,
9.17. Try to show the sequence in 9.5 is bounded and monotone.
- Due 9/16. Read section 8 and do problems 8.1, 8.2e, 8.5, 8.6. Read section 9 and do problems
9.1a, 9.2., 9.5 (hint: take limit of both sides of the given equation).
- Due 9/11. Read sections 4 and 5. Do problems 4.4 b,e,k,n, 4.8, and
problems 5.1 and 5.2. Without reading section 7 yet, try problems 7.3
a,d,n,t, 7.4 (using your memories from calculus).
- Due 9/9. Read pages 13-18. Do problems 3.5, 3.6. (Be aware of
of properties of real numbers from this section, 3, but we will not be
focusing on the study of ordered fields). Read section 4 and do problems
4.1 part b,e,k,n and 4.3 part b,e,k,n.
- Due 9/4. Read pages 365-366 (on set notation) and pages 1-13. Do problems
in section 1 (page 5) #1.2, 1.7, 1.9, 1.11, and in section 2 (page 12)
#2.4, 2.8.
- Due now: be sure you are registered for the 1 credit independent study. You may need to remove a hold on your account before registering.
Course Information:
This course is an introduction to the theory of functions of a real
variable. Topics include real numbers and the completeness property, limits
of sequences, elementary topological concepts, continuity and uniform
continuity, sequences and series of functions, derivatives, Taylor's theorem
and the Riemann integral. It is a pre-requisite that you have taken MATH 201.
- Location: Mondays and Wednesdays, 10:05-11:55, Kiely Hall Rm 320.
- Textbook: "Elementary Analysis, the Theory of Calculus" 2nd Edition, by
Kenneth A. Ross.
- Grading: The final grade will be based on two preliminary exams (30%
each), and the final exam (40%).
- Exams: The two preliminary exams are in class on Monday Sept. 30th and
Wednesday Nov. 6th.
The final exam is: TBA.
The expected course outcome is for the student to learn this material and demonstrate their level of mastery on the course assessments. This should be accomplished by being an active participant in class, completing all of the assignments, studying independently and in groups outside of class, and seeking my help as needed.
Contact Information:
- Instructor: Scott Wilson
- Email: scott dot wilson AT qc.cuny.edu
- Office hours: Mon 12:45-1:30 (Kiely 609) and Wed 12:40-1:25 (Kiely 331-
Math Lab), or by appointment.
- Office: Kiely 609
Academic Integrity:
In case of cheating or plagarism, I will seek
academic and disciplinary sanctions. See The CUNY Policy on Academic Integity.
Reasonable Accommodations for Students with Disabilities:
Candidates with disabilities needing academic accommodation should: 1)
register with and provide documentation to the Office of Special Services,
Kiely Hall Room 108; 2) bring a letter indicating the need for accommodation
and what type. This should be done during the first week of class. For more
information about services available to Queens College candidates, visit Office of Special Services for Students with Disabilities in Kiely Hall Room 108 or contact the Director, Dr. Miriam Detres-Hickey at QC.SPSV@qc.cuny.edu.
Statement on Student Wellness:
As a student, you may experience a range of challenges that can interfere with
learning, such as strained relationships, increased anxiety, substance use,
feeling down, difficulty concentrating and/or lack of motivation. These mental
health concerns or stressful events may diminish your academic performance
and/or reduce your ability to participate in daily activities. QC services are
available free of charge. You can learn more about confidential mental health
services available on campus at Counseling Services Department.
Course website: https://qcpages.qc.cuny.edu/~swilson/math310.html