Information on the
Basic Exam
1. MS Basic Exam
Format:
Each exam consists of a 2-hour written exam, a
take-home exam, and an oral discussion on the take-home part.
2. MS Basic Exam Schedule:
The exam will be given on the Friday before each
Semester (Fall and Spring) starts whenever there are
MS students enrolled in the program. The take-home part should be turned in by
noon of the Tuesday of the first week of the semester. The oral discussion will
be scheduled on the Thursday of the first week of the semester.
3. Content of the MS Basic Exam
(a) Topics to be
covered in the MS Basic Advanced Calculus Exam:
Elementary properties of
Open/closed/compact/connected sets in R^n. Numerical
sequences and series. Limits, Cauchy sequences, convergence.
Continuity. Continuity and
compactness/connectedness. Uniform continuity.
Sequences and series of
functions; uniform convergence. Calculus of real-valued
functions: Differentiation, mean value theorems,
(b) Topics to be
covered in the MS Basic Linear Algebra Exam:
Vector spaces, linear independence, basis,
dimension, linear transformation, and matrix representations, rank, range
space, null space, eigenvalues and eigenvectors,
diagonalizations, canonical forms, inner
product spaces, othogonal basis, symmetric and hermitian
matrices and properties.
4. Grading of the MS Basic Exam
The examination committees will send the
graduate program committee their course recommendations within a 7 day period
after the written exam is conducted. These may include advanced calculus Math
451, or real analysis Math 551 and/or linear algebra Math 343, Math 441, Math
543. The recommendation will be based on the student’s background, and
performance on the exam.
Textbooks:
Advanced Calculus
Elementary
Analysis: The Theory of Calculus, by Kenneth Ross (used for Math 451)
Principles of Mathematical Analysis,
Rudin (a standard advanced calculus text)
Linear Algebra
Elementary
Linear Algebra, Kolman (used for
undergraduate linear algebra)
Introduction
to Linear Algebra, Strang (used for applied linear
algebra)
Linear
Algebra, Hoffmann & Kunze (used for graduate
linear algebra)