MA360, Lia Vas --
SYLLABUS
1. Prerequisites:
MA201. MA202 recommended but not required.
2. Since the
course is mostly based on material covered in class handouts and classwork, it is absolutely imperative that students
attend classes. Students are responsible for all material covered in
class, even if attendance is not checked or assignments collected. There will
be 3 assignments and one student project
+ presentation. No assignment grade will be dropped. Assignments
turned in after their due date will receive an automatic reduction in grade.
Tentative Schedule:
1.
Recursive formulas in Chemistry. Programming in MATLAB and
on TI83 (3.5 weeks)
2.
Groups, Symmetry Groups o f Molecules, (4.5 weeks)
3.
Fourier Series, Complex Functions, Fourier Transform (4
weeks)
4.
Presentations, Guest Speakers (2 weeks)
Course is based on:
1. Mathematical Physics, Eugene Butkov, Addison-Wesley, 1968.
2. Analytical Chemistry, Alan L. Foly,
3. Symmetry and Structure, S.F.A. Kettle, John Wiley & Sons,
1986.
4. When Topology Meets Chemistry, Erica Flapan,
5. various websites (details in handouts)
3.
Course Objectives: to obtain a well rounded introduction to the various
areas of mathematics especially those mostly needed for applications to
chemistry and/or medical imaging. The course will be covering the following
three topics:
1. Fourier Transform.
Students will learn about the Fourier transform and will find out why it is
used widely in nuclear magnetic resonance, spectroscopy, magnetic resonance
imaging and signal processing.
2. Groups and
Symmetries of Molecules. Group theory is a very powerful mathematical tool used
in quantum chemistry and spectroscopy. Students will be exposed to the idea of
using the geometric structure of a molecule to conclude something about
electronic structure. Students will also learn the basics of topology and
algebraic topology and how the group theory is used to obtain information about
a space of interest.
3. Recursive formulas
in Chemistry. Students will learn about basics of programming and will write
programs for TI83 calculators and programs in MATLAB that will model certain
chemical equations.
Learning outcomes:
1. The course gives the students a
deeper insight into the material learned in certain chemistry courses and
better understanding of various techniques used in research in chemistry and medical
imaging. The student will also acquire knowledge of various mathematical
concepts and modeling techniques required for successful application of
mathematics in chemistry and medical imaging.
2. For students interested in continuing their education at a
graduate level, it provides them with mathematical techniques that certain
graduate programs in chemistry use.
3. It involves the students in the interaction of two
different fields. A student interested in a career in science is likely to be a
part of a research team consisting of different professionals. The material
exposed in the course will enable students to better interact with other
members of that team. Also, the students will visit the Laboratory for
Structural NMR Imaging at the
4. The course emphasizes research ideas, not just mastering
various techniques or methods. The underlying theme behind all course topics (Fourier
Transform, Groups and Symmetries and applications of recursive equations) is that it might be easier to solve
a certain problem by translating it to a different field, solving it there and
then translating the solution back into the original setting. This general
principle of problem solving is often used in various fields and will be a
useful concept for the students to acquire.
4. Academic integrity:
Academic integrity is at the center of the educational experience at USP.
Students are therefore expected to uphold the highest
standards of academic integrity and not engage in nor tolerate academic
dishonesty. Academic dishonesty includes, but is not limit to, fabrication,
cheating or plagiarism. Any violation of academic integrity will be
investigated and, where warranted, the student will receive appropriate
sanctions through the University's Student Conduct Process. Please familiarize
yourself with the current USP Student Handbook. In particular, adherence to the
Student Conduct Policy and Academic Integrity Policy will help to ensure that your learning and living experiences are founded on
integrity.
Any academic dishonesty,
including but not limited to academic dishonesty on assignments and exams,
might result in an “F” grade for the course and may also be subject
to disciplinary action. Please read the Student Conduct Policy on pages
27 – 35 of the student handbook.
5. Americans
with Disabilities Act (