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New York City College of Technology The City University of New York
DEPARTMENT: Mathematics
PREPARED BY: Professors H. Carley and N. Katz
COURSE: MAT 3075
TITLE: Introduction to real analysis
DESCRIPTION: This course is an introduction to analysis of real functions of one variable with a focus on proof. Topics include the real number system, limits and continuity, differentiability, the mean value theorem, Riemann integral, fundamental theorem of calculus, series and sequences, Taylor polynomials and error estimates, Taylor series and power series.
TEXT: M. Spivak, Calculus 4th Ed., Publish or Perish Press, Houston Texas, 2008.
CREDIT HOURS: 4 cl hrs, 4 cr
PREREQUISITES: MAT 1575; and MAT 2070 or MAT 2071
LEARNING OUTCOMES:
- Students will be able to formulate key concepts in real analysis with mathematical precision.
- Students will be able to state the hypothesis and conclusions of basic theorems in real analysis and apply them in proofs.
INSTRUCTIONAL OBJECTIVES AND ASSESSMENT:
INSTRUCTIONAL OBJECTIVES ASSESSMENT
For successful completion of the course, Instructional Activity, Evaluation students should be able to: Methods and Criteria list limit and order properties of real numbers and use those properties to prove results about subsets of real numbers
class discussion, written assignments, class presentations and in class examinations
prove that a limit does or does not exist class discussion, written assignments, class presentations and in class examinations prove continuity or uniform continuity of a function
class discussion, written assignments, class presentations and in class examinations formulate the construction of the Reimann integral and prove basic facts about its properties.
class discussion, written assignments, class presentations and in class examinations
find approximation of functions using Taylor polynomials including estimation of error
class discussion, written assignments, class presentations and in class examinations
check a sequence of functions for point- wise and uniform convergence
class discussion, written assignments, class presentations and in class examinations
GENERAL EDUCATION LEARNING OUTCOMES
ASSESSMENT
Gather, interpret, evaluate, and apply information discerningly from a variety of sources.
Classroom discussion, writing assignments, student presentations, problem sets, tests, exams. Employ scientific reasoning and logical thinking.
Classroom discussion, writing assignments, student presentations, problem sets, tests, exams. Acquire tools for lifelong learning. Classroom discussion, writing assignments, student presentations, tests, exams. Use creativity to solve problems. Problem sets, group work. Show curiosity and the desire to learn. Classroom discussion, groups work, presentations.
GRADING PROCEDURE:
Written Assignments, Presentations, 3 Term Tests, Final Exam
TEACHING/LEARNING METHODS:
l Lecture and guided discussion in class l Homework, written assignments l Discussion outside class, student presentations.
