Syllabus for Math 432 (Real Analysis)
Spring 2023 Semester at Lycoming College
Course Content
MATH 432 is an introduction
to the rigorous analysis of concepts in calculus. Topics include the construction of the
natural numbers, the integers, and the rational numbers; issues involved with
the construction of the real numbers; limits; convergence of sequences and
series; the topology of the Euclidean plane; continuity; differentiability;
integration. Prerequisites: MATH 238 and
a grade of C or better in MATH 234.
Course Goals
Goals for this course include
developing critical thinking skills while acquiring the background both in
content and mathematical maturity required for more advanced courses in pure
and applied mathematics; specifically, students should be able to demonstrate
greater understanding and insight into the rational number and real number
fields, limits, continuity, differentiability, integration, and convergence
than gained in typical Calculus I and II courses.
Who Should be Taking This Course
This course a requirement for
the mathematics major. The prerequisites
are MATH 238 (Multivariable Calculus) and a grade of C or better in MATH 234
(Foundations of Mathematics).

OFFICE
HOURS Find your instructor’s office hours at http://lycofs01.lycoming.edu/~sprgene/OffHrs.htm
, and write them here for
future reference. 

Grading
Item 
Point
Values and Policies 
Homework 
Homework
assignments due on the next class are posted in red
on the course schedule. Answers to
homework become available immediately after it is due, so late homework is
never accepted for any reason; at least some missed homework points can be
earned back by doing certain practice exercises posted on the course schedule, and students not missing too many homework points
can still have a perfect or near perfect homework average. Homework
counts for 25% of the final grade; however, a student who misses submitting
more than 10 homework assignments automatically fails the course. 
Semester Exams 
Several
semester tests are given, one about every three or four weeks; specific dates
are available from the course schedule. For each
missed test, a grade of zero is recorded, unless (1) the instructor is
presented with documented evidence of a medical reason for not completing the
test at the scheduled time, and (2) arrangements to make up the test are
made within 24 hours of the originally scheduled exam time. Semester
exams count for 50% of the final grade. 
Final
Exam 
The
final exam (administered during final exam
week) counts for 25% of the final
grade. 
Attendance 
The
final course grade percentage is reduced by 4% for each unexcused absence
after the third unexcused absence; an absence is considered to be excused
when the instructor accepts an email from the student explaining the reason
for the absence. It is the student’s
responsibility to find out what was missed in class and keep up with the
coursework. A copy of class notes is
made available after each class. A student with more than 8 unexcused
absences automatically fails the course. 
The
final course letter grade is determined from the course average as follows: A = above 93.33% A–
= 90% to 93.33% B+
= 86.67% to 90% B = 83.33% to 86.67% B–
= 80% to 83.33% C+
= 76.67% to 80% C = 73.33% to 76.67% C–
= 70% to 73.33% D+
= 66.67% to 70% D = 63.33% to 66.67% B–
= 60% to 63.33% F
= below 60% 
Disability
Support Services
In keeping
with the Americans with Disabilities Act (and its amendments) and Section 504
of the Rehabilitation Act, Lycoming College is committed to providing
reasonable accommodations for students with documented disabilities that
impact their learning experiences. The Office of Academic Services Deans
coordinates disability support services (DSS), and students can contact (570)
3214358 or academicservices@lycoming.edu to set up a confidential conversation about the
disclosure and accommodation process. The Office of Academic Services Deans
is located in the second floor of the Krapf Gateway
Center. Further information regarding DSS is available at: https://www.lycoming.edu/academicresourcecenter/disabilitysupport/. 
Required Materials
Each student must have
· a threering binder containing copy of this syllabus, the
course schedule, the class notes, completed assignments, etc. (Note: Since
students will need to use this binder every day in class and might be
allowed to use this binder for some exams, the binder should be kept up‑to‑date
and complete.) Although no textbook is
required, there will be references made during the course to the materials
produced here
by N. J. Wildberger and to Introduction to Real Analysis by William F. Trench available here.
Course Links
Some WellKnown Sums and
Series
Tips for Success in This Course
(1) Keep up with the homework
 understanding every homework assignment as completely as you can is the key
to grasping the course material. Even
though there will be some homework assignments that you may not be required to
submit, do them anyway, since they will help you master the material.
(2) Keep your binder
uptodate and wellorganized, since you might be allowed to use the binder for
exams.
General Standards and Policies
All work submitted must be of
professional quality. All paper must be
neat, without ragged edges, rips, tears, smudges, stains, etc. All answers must be clear, complete, and
concise; handwriting must be legible. If
the instructor can't read it, it's wrong.
Assignments may be downgraded if these standards are not met.
It can be very helpful for
some students to work together on daily assignments and to study together; this
is encouraged when it does not result in one student simply copying another's
work with no understanding. Acts of
academic dishonesty will result in a grade of F for the course, and a letter to
the Dean describing the circumstances.
If you are having problems in the course, talk to the instructor; don't
involve yourself in academic dishonesty. With each assignment submitted,
students are expected to write a short note at the end of the assignment
indicating from whom help was received and to whom help was given (but this
does not affect the grade for the assignment).
The following is from the FACULTY HANDBOOK in the section titled Student
Course Load:
"It is expected that
students will spend, in preparation for courses, two hours of study time
outside the classroom for every hour of credit in the classroom."
This means that you should be
prepared to spend, on average, eight hours per week outside of class working on
a fourcredit course; however, this will vary from student to student and from
course to course. Your time will be
spent reading the text, reviewing class notes, and completing homework
exercises.