General Course Information for MTH640: Real Analyses

Course: MTH640 - Real Analyses
Textbook: For the correct edition of the textbook assigned to a specific class, go to:

Course Prerequisite(s):
Course Description: Topics include real and complex number systems, elements of point-set topology of Euclidean space, numerical sequences and series, continuity and differentiability for functions of one and several variables. The Riemann-Stieltjes integral as a generalization of the Riemann integral, sequences and series of functions, and Fourier series will be studied as well.
Course Learning Outcomes:
  • Evaluate ordered sets, real and complex fields
  • Apply main concepts of metric spaces and their topology to concrete problems
  • Interpret the connectedness, compactness and Weierstrass theorem
  • Evaluate the Cauchy sequences, completeness of real numbers, convergence and absolute convergence of series
  • Interpret concepts of limits, continuity of functions in metric spaces, and their properties, differentiation and integration
  • Interpret uniform convergence of functions and Stone-Weierstrass theorem
  • Evaluate the use of special functions
  • Elaborate the Contraction Mapping Theorem, The Inverse Function and the Implicit Function Theorems.
Specified Program Learning Outcomes:
    • Analyze the research results and data on curricular materials, content, teaching methods, and new trends in mathematics education.
    • Based on acquired advanced mathematical abilities analyze and evaluate main principles of general mathematics and mathematics education.
    • Conduct original research in mathematics education and related mathematical content areas.
    • Evaluate primary research in mathematics education and related areas, including the identification of strengths and weaknesses of studies.
    • Propose and employ new robust and theoretically grounded approaches, methods and curricular related researches in teaching mathematics.

Students with Disabilities:
Students seeking special accommodations due to a disability must submit an application with supporting documentation, as explained under this subject heading in the General Catalog. Instructors are required to provide such accommodations if they receive written notification from the University.

Writing Across the Curriculum:
Students are expected to demonstrate writing skills in describing, analyzing and evaluating ideas and experiences. Written reports and research papers must follow specific standards regarding citations of an author's work within the text and references at the end of the paper. Students are encouraged to use the services of the University's Writing Center when preparing materials.

The following website provides information on APA, MLA, and other writing and citation styles that may be required for term papers and the like:

National University Library:
National University Library supports academic rigor and student academic success by providing access to scholarly books and journals both electronically and in hard copy. Print materials may be accessed at the Library in San Diego or through document delivery for online and regional students. Librarians are available to provide training, reference assistance, and mentoring at the San Diego Library and virtually for online or regional students. Please take advantage of Library resources:


Contact the Library:

  • (858) 541-7900 (direct line)
  • 1-866-NU ACCESS x7900 (toll free)

Use the Library Training Tools (on the Library Homepage) for additional help

  • Recorded class presentations
  • Tutorials & Guides (APA/MLA, Peer-Review, and more)

Plagiarism is the presentation of someone else's ideas or work as one's own. Students must give credit for any information that is not either the result of original research or common knowledge. If a student borrows ideas or information from another author, he/she must acknowledge the author in the body of the text and on the reference page. Students found plagiarizing are subject to the penalties outlined in the Policies and Procedures section of the University Catalog, which may include a failing grade for the work in question or for the entire course. The following is one of many websites that provide helpful information concerning plagiarism for both students and faculty:

Ethical behavior in the classroom is required of every student. The course will identify ethical policies and practices relevant to course topics.

Students are expected to be competent in using current technology appropriate for this discipline. Such technology may include word processing, spreadsheet, and presentation software. Use of the internet and e-mail may also be required.

Learning to work with and value diversity is essential in every class. Students are expected to exhibit an appreciation for multinational and gender diversity in the classroom.

As a diverse community of learners, students must strive to work together in a setting of civility, tolerance, and respect for each other and for the instructor. Rules of classroom behavior (which apply to online as well as onsite courses) include but are not limited to the following:

  • Conflicting opinions among members of a class are to be respected and responded to in a professional manner.
  • Side conversations or other distracting behaviors are not to be engaged in during lectures, class discussions or presentations
  • There are to be no offensive comments, language, or gestures