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MS Basic Exam for Advanced Calculus and Linear Algebra

M.S. Basic Exam for Advanced Calculus and Linear Algebra

About the M.S. Basic Exam

Each exam consists of a 2-hour written exam, and a take-home exam.

Schedule

The exam will be given prior to the start of each Fall semester. The take-home part will be due several days later. Results and recommendations will be provided prior to the end of the add/drop period. .

Content of the M.S. Basic Exam

Topics to be covered in the M.S. Basic Exam Advanced Calculus include the following:

  • Elementary properties of Open/Closed/Compact/Connected sets in R^n
  • Numerical sequences and series
  • Limits, Cauchy sequences, and convergence
  • Continuity
  • Continuity and compactness/connectedness
  • Uniform continuity
  • Sequences and series of functions; uniform convergence
  • Calculus of real-valued functions: Differentiation, mean value theorems, Taylor's theorem
  • Definition and existence of the Riemann integral
  • Fundamental Theorem of Calculus
  • Integration and differentiation of series/sequences of functions

Topics to be covered in the M.S. Linear Algebra Exam include the following:

  • Vector Spaces
  • Linear Independence
  • Basis
  • Dimension
  • Linear Transformation
  • Matrix Representations
  • Rank
  • Range Space
  • Null Space
  • Eigenvalues and eigenvectors
  • Diagonalizations
  • Canonical forms
  • Inner product spaces
  • Orthogonal basis
  • Symmetric and Hermitian matrices and properties

Grading of the M.S. 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

  1. Elementary Analysis: The Theory of Calculus by Kenneth Ross (Used for Math 451)
  2. Principles of Mathematical Analysis by Rudin (A standard Advanced Calculus Text)

Linear Algebra

  1. Elementary Linear Algebra by Kolman (Used for Undergraduate Linear Algebra)
  2. Introduction to Linear Algebra by Strang (Used for Applied Linear Algebra)
  3. Linaer Algebra by Hoffman and Kunze (Used for Graduate Linear Algebra)

Please send any questions or comments to gradprog@math.wvu.edu