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Introductn to the Theory of Functions I


MATH 765 and MATH 766 are theoretical courses on the fundamental concepts of analysis and the methods of proof. These two courses include the concept of a real number; limits, continuity, and uniform convergence; derivatives and integrals of functions of one and of several real variables.


Intro to Analysis, Wade, Prentice Hall, 4th edition.


MATH 223 and MATH 290 or equivalent.

Credit Hours: 


  1. The Real Number System
    • Field properties, well-ordering and completeness
    • Sequences and Bolzano-Weierstrass theorem
    • Functions and countability
  2. Continuity and Differentiability on the Real Line
    • Limits, continuity and uniform continuity
    • Differentiability, mean value theorem and monotonicity
  3. The Riemann Integral
    • The Riemann integral and Riemann sums
    • The fundamental theorem of calculus, integration by parts and change of variables
    • Improper Riemann Integrals
  4. Infinite Series
    • Convergence, absolute convergence and tests of convergence

(Torres 2017 )

Every Fall Semester

Events Calendar

Using Math

CTE course transformation grant helps Emily Witt, assistant professor of math, develop active learning with student groups in calculus.  Positive results using modules developed with Justin Lyle and Amanda Wilkens, math graduate students, were attained.  Read more

Math and COVID-19: Sources on how math is being used to track the virus and its spread.  AMS link.

A mathematician-musician's breakthrough melds East, West. Read more.

Researcher's innovative approach to flood mapping support emergency management and water officials. Read more.

Nicole Johnson found a way to express her baton twirling using math. See video.