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).












Find your instructor’s office hours at , and write them here for future reference.







Point Values and Policies


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.


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) 321-4358 or 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:



Required Materials

Each student must have

·      a three-ring 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


Course Schedule


Some Well-Known Sums and Series


A Useful Trigonometry Review



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 up-to-date and well-organized, 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 down-graded 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 four-credit 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.