Course Content (Under Construction)

The goal of the course is to give an introduction to the level of rigor and care that is used in mathematical proof and reasoning throughout mathematics. We take as our subject matter for this undertaking a more careful study of limits, sequences, series, power series than is the usual case in the calculus sequences (which are prerequisites for the class). So we will be interested in understanding both results and methods. As such the course hopefully will be a useful gateway to future study in mathematics as well as reinforcing and refining results and material you may have already seen in earlier courses. We begin with a brief study of the formal, logical underpinnings of mathematical reasoning. We then spend time with mathematical induction, a basic basic property of integers Then we look at real numbers and the essential property called the completeness property of real numbers. This leads in a natural way into studies of limits for sequences and series. A major application will then be to power series and their use in approximation of functions via the Taylor series and using power series as an important tool in studying differential equations and their solutions.

Basic Course Information

Math 2283 is a 3 credit course. Here is the official mathematics department description of this course:

MATH 2283 - Sequences, Series, and Foundations Introduction to mathematical reasoning used in advanced mathematics. Elements of logic. Mathematical induction. Real number system. General, monotone, recursively defined sequences. Convergence of infinite series/sequences. Taylor's series. Power series with applications to differential equations. Newton's method.

Lecture: 010 LEC , 12:20 PM - 1:10 PM , M,W 45 Rapson Hall , TCEASTBANK .
Instructor: Professor S.Sperber.
Email: sperber@umn.edu
Office: 457 Vincent Hall
Phone: 612-625-4374
Office Hours: Tuesday 11-12, Wednesday 2-3PM
Textbook: Sequences, Series and Foundations Mathematics 2283, Wayne Richter, (can be purdhased through Alpha Print)

Recitation: Cecily Santiago.
Office: 555 Vincent Hall Phone: 612-624-2527 Email: santi198@umn.edu

-011-DIS, 12:20PM - 1:10PM, Tu,Th Vincent Hall 20, TCEASTBANK
-012-DIS, 1:25AM - 2:15PM, Tu,Th Vincent Hall 311, TCEASTBANK

Prerequisites

Math 2263/2373 and Math 2264/2374 (or department approved equivalents)

Organization of Course and Grading Policy

There will be two mid-semester in-class exams of 50 minute duration. Exams will be held in lecture class on Monday, February 24 and Monday, March 30.

There is also a (cumulative) final examination which will be given (date and location to be filled in)

Homework will be collected weekly, every Tuesday in recitation and some, if not all, of your work on each problem set will be graded. This grade will be a component of the 20% of the "homework and class participation" portion of your Final grade. Attendance is not required but class performance can help final grade. The gradeline for final grade will be curved and we will set a final grade gradeline after final has been graded. An approximate gradeline will be given after each exam and for homework/class.

Students are encouraged to work on homework together or with other students. But the work submitted should be in the end your own. Scholastic dishonesty is not permitted. See policies at https://policy.umn.edu/education#Education

The final grade will be determined according to the following guide:

mid-semester exams 40%

final 40%

homework and class participation 20%