MATH 409 – Advanced Calculus I
SPRING 2016, SECTION 501
Instructor’s Information
Instructor: Paul Skoufranis
E-mail: pskoufra at math.tamu.edu
Office: Blocker 525D
Offices Hours: Mondays from 11:30AM to 1:50PM, 4:10PM to 5:20PM, and by appointment
Administrative Information
Course Prerequisites: MATH 220 and MATH 221
Course Webpage: http://www.math.tamu.edu/~pskoufra/S2016-MATH409.html
Common Course Webpage: http://www.math.tamu.edu/courses/math409/
Lectures: MWF from 9:10AM to 10:00AM in Blocker 164
Help Sessions: Mondays, Tuesdays, Wednesdays, and Thursdays, 7PM to 9:30PM in Blocker 111
Textbook: An Introduction to Analysis, fourth edition, William R. Wade (recommended)
Test Dates:
Test One à Friday February 26, 2016, in class
Test Two à Wednesday April 13, 2016, in class
Final Examination Dates: Friday May 6, 2016, 8:00AM to 10:00AM, Blocker 164
Course Description and Objectives
Throughout history, calculus has been an essential branch of mathematics with plentiful real-world
applications ranging from the construction of buildings to models for the motion of celestial objects.
However, many blunders have occurred in the theory of calculus. These errors materialized since results
that were impossible to demonstrate seemed intuitively correct and thus were assumed to be fact. As
these inaccuracies were sought out and corrected, a new branch of mathematics known as real analysis
was developed to rigorously study the real numbers and functions on the real numbers.
This course will reintroduce students to calculus through the lens of rigorous mathematics. We will
begin by studying the properties that define the natural numbers and the real numbers. This leads to the
essential study of sequences of real numbers and what it means for a sequence of real numbers to
converge. Subsequently, we will discuss a range of topics including types and properties of subsets of
real numbers, and the various magnitudes of infinity. Our focus will then turn to the fundamental
concepts of calculus, including continuous functions, differentiability, and the Riemann integral.
This course will be different in nature to the calculus courses students have taken in the past.
Specifically there are two main focuses of this course. The first is to rigorously develop the above
mathematical concepts. This is essential as students are familiar with many of the above topics from
other calculus courses, yet do not possess precise definitions of these concepts which may lead to errors.
The second main focus of this course is to introduce students to the types of mathematical proof used in
real analysis. The techniques developed in this course are essential tools students will be required to have
in their repertoire in order to proceed with the study of analysis.
Course Schedule
The following is a rough outline of the chapters and schedule for the lectures of this course:
1. Axioms of Number Systems (5 lectures)
2. Sequences of Real Numbers (6 lectures)
3. Topology of the Real Numbers (4 lectures)
4. Cardinality of Sets (4 lectures)
5. Continuity (6 lectures)
6. Differentiability (8 lectures)
7. The Riemann Integral (5 lectures)
8. Series (if time permits)
(Note the above is a rough and there are 2 lectures not accounted for in the above outline.)
Grading Scheme
A student’s final grade in the course will be computed as follows:
20% Homework + 40% Tests (20% Each) + 40% Final Examination
A student’s final letter grade will be determined by the rule 90-100 for an A, 80-89 for a B, 70-79 for a C,
60-69 for a D, 0-59 for an F. To pass the course, a student must take the final examination.
Homework
The purpose of the homework in this course is to aid students in the comprehension of the material
presented in lecture each week and to expand students’ knowledge beyond what can be covered in
lectures. Thus the instructor will endeavour to provide students with a sufficient amount of time after the
material is presented in lecture for completion of the homework.
There will be eleven homework assignments in this course where the lowest grade will not count
towards a student’s final grade. Homework will be posted on the course webpage at least one week prior
to the due date. Homework will be due in class on the due date and late homework will not be accepted,
as solutions will be posted promptly. Students are expected to clearly indicate their names and student ID
number on their homework.
Students are welcome to collaborate with each other on the homework. However, each student must
write his or her solutions separately in their own words (no copying!).
Regrading
A student that believes there has been an error in the grading of their work should bring it to the attention
of the instructor within one week from the time at which the work was returned to the class. Objections
that arise after this one-week period will not be considered.
Academic Integrity
“An Aggie does not, lie, cheat, or steal, or tolerate those who do."
Copying work done by others, either in-class or out of class, is an act of scholastic dishonesty and will be
prosecuted to the full extent allowed by University policy. See http://aggiehonor.tamu.edu for more
information.
Make-up Policy
In accordance with university regulations, make-ups for missed exams and assignments will only be
allowed for a university-approved excuse in writing. Whenever possible, students should inform the
instructor before an exam or assignment is missed. Students are required to notify the instructor by the
end of the next working day after missing an exam or assignment. Otherwise, they forfeit their rights to a
make-up.
Support Services
The Americans with Disabilities Act (ADA) is a federal anti-discrimination statute that provides
comprehensive civil rights protection for persons with disabilities. Among other things, this legislation
requires that all students with disabilities be guaranteed a learning environment that provides for
reasonable accommodation of their disabilities. If you believe you have a disability requiring an
accommodation, please contact Disability Services, currently located in the Disability Services building at
the Student Services at White Creek complex on west campus or call 979-845-1637. For additional
information, visit http://disability.tamu.edu.