Math 310-0101: Introduction to Proof in Analysis - Spring 2020 Revised Mar 25

Instructor: Professor Steve Halperin

Contact Information:

Email: shalper@umd.edu.

Office: Only available by Zoom.

Phone: 301-405-1875 (from any campus phone dial 58175)  Note: This is unavailable while I am not allowed on campus

Course webpage:  http://www.math.umd.edu/~shalper/Math310-0101.html

Key to Success:  A fundamental strategy in this course is to ask questions: in class, during office hours, or by email. The resulting student-teacher exchange can be critical to the learning process.

Textbook: The textbook is posted at Text.

Outline of the Course:

The course will cover most of the material in the online textbook  as described below:

Chapter 1 Introduction
Purpose
Expectations

Chapter 2 Mathematical Proofs
The Language of Mathematics
What is a Proof in Mathematics?
Solving a 310 Problem
Sets, Numbers, and Sequences
Sums, Products, and the Sigma and Pi Notation
Logical Expressions for Proofs
Examples of Mathematical Statements and their Proofs
The True or False Principle: Negations, Contradictions, and
Counterexamples
Proof and Construction by Induction
Polynomials
The Literature of Mathematics

Chapter 3 Basic Set Theory
Sets
Operations with Sets
Maps between Sets
Composites, the Identity Map, and Associativity
Onto, 1-1, and 1-1 Correspondences

Chapter 4 The Real Numbers
Properties of the Rational Numbers
The Real Numbers, Inequalities, and the Sandwich Theorem
Absolute Value
Bounds
Least Upper and Greatest Lower Bounds
Powers
Constructing the Real Numbers

Chapter 5 Infinite Sequences
Convergent Sequences
Bounded Sequences
The Cauchy Criterion for Convergence
The Intersection Theorem
Subsequences

Chapter 6 Continuous Functions of a Real Variable
Real-valued Functions of a Real Variable
Limits
Limits and Negations
Limits of Sequences and Limits of Functions
Continuous Functions
Continuous Functions Preserve Intervals

Office Hours: These are now online and the times and contact procedure will be posted shortly.

Additionally, during the week  I am usually available via Zoom and students are welcome make a Zoom appointment using the procedure you will receive shortly!

Lecture Classroom on line via Zoom.. The Zoom meetings are already scheduled.

Lectures: MWF 9-9:50 (NOTE these times will remain the same!)

Calculators:
Calculators are irrelevant to this course. All devices with an on/off switch, including calculators, cell phones and all other portable devices, must be turned off and inaccessible during quizzes and exams.

Classroom rules: These will be sent soon.

Help Sessions: TBD

Exams: There will be three midterm tests and one final exam. All test and exam questions will be taken from the exercises in the text. Information about these will be posted at Homework, Midterms, and Exam  and in Zoom.The midterm tests will be held via Zoom and You will be informed in advance of the procedure. Tests and exams must be submitted in  ink or typed.

Except in emergency cases students must request and receive approval for an excused absence before the test. In the case of absences such as religious observances known at the beginning of the semester, the student must make the request during the schedule adjustment period.

Midterm 3: Fri. May 1

Cheating:  Students who cheat will be prosecuted according to the university regulations

Academic integrity: The university expects all students to adhere to the University Honor Pledge: "I pledge on my honor that I have not given or received any unauthorized assistance on this assignment/ examination."

Disabilities: Students who require special examination conditions must register with the office of the Disabled Students Services (DSS) in Shoemaker Hall. Documentation must be provided to the instructor at the start of the semester. Proper forms must be filled and provided to the instructor before every exam.

Campus undergraduate student/course policies and procedures:  http://www.ugst.umd.edu/courserelatedpolicies.html

Instructor: Professor Steve Halperin

Contact Information:

Email: shalper@umd.edu.

Office: second floor of the Math Building, Room 2107.

Phone: 301-405-1875 (from any campus phone dial 58175)  Note: This is unavailable while I am not allowed on campus

Course webpage:  http://www.math.umd.edu/~shalper/Math310-0101.html

Key to Success:  A fundamental strategy in this course is to ask questions: in class, during office hours, or by email. The resulting student-teacher exchange can be critical to the learning process.

Textbook: The textbook is posted at Text.

Outline of the Course:

The course will cover most of the material in the online textbook  as described below:

Chapter 1 Introduction
Purpose
Expectations

Chapter 2 Mathematical Proofs
The Language of Mathematics
What is a Proof in Mathematics?
Solving a 310 Problem
Sets, Numbers, and Sequences
Sums, Products, and the Sigma and Pi Notation
Logical Expressions for Proofs
Examples of Mathematical Statements and their Proofs
The True or False Principle: Negations, Contradictions, and
Counterexamples
Proof and Construction by Induction
Polynomials
The Literature of Mathematics

Chapter 3 Basic Set Theory
Sets
Operations with Sets
Maps between Sets
Composites, the Identity Map, and Associativity
Onto, 1-1, and 1-1 Correspondences

Chapter 4 The Real Numbers
Properties of the Rational Numbers
The Real Numbers, Inequalities, and the Sandwich Theorem
Absolute Value
Bounds
Least Upper and Greatest Lower Bounds
Powers
Constructing the Real Numbers

Chapter 5 Infinite Sequences
Convergent Sequences
Bounded Sequences
The Cauchy Criterion for Convergence
The Intersection Theorem
Subsequences

Chapter 6 Continuous Functions of a Real Variable
Real-valued Functions of a Real Variable
Limits
Limits and Negations
Limits of Sequences and Limits of Functions
Continuous Functions
Continuous Functions Preserve Intervals

Office Hours: These are now online and the times and contact procedure will be posted shortly.

Additionally, during the week  I am usually available via Zoom and students are welcome make a Zoom appointment using the procedure you will receive shortly!

Lecture Classroom on line via Zoom.. The Zoom meetings are already scheduled.

Lectures: MWF 9-9:50 (NOTE these times will remain the same!)

Calculators:
Calculators are irrelevant to this course. All devices with an on/off switch, including calculators, cell phones and all other portable devices, must be turned off and inaccessible during quizzes and exams.

Classroom rules: These will be sent soon.

Help Sessions: TBD

Exams: There will be three midterm tests and one final exam. All test and exam questions will be taken from the exercises in the text. Information about these will be posted at Homework, Midterms, and Exam  and in Zoom.The midterm tests will be held via Zoom and You will be informed in advance of the procedure. Tests and exams must be submitted in  ink or typed.

Except in emergency cases students must request and receive approval for an excused absence before the test. In the case of absences such as religious observances known at the beginning of the semester, the student must make the request during the schedule adjustment period.

Midterm 3: Fri. May 1

Cheating:  Students who cheat will be prosecuted according to the university regulations

Academic integrity: The university expects all students to adhere to the University Honor Pledge: "I pledge on my honor that I have not given or received any unauthorized assistance on this assignment/ examination."

Disabilities: Students who require special examination conditions must register with the office of the Disabled Students Services (DSS) in Shoemaker Hall. Documentation must be provided to the instructor at the start of the semester. Proper forms must be filled and provided to the instructor before every exam.

Campus undergraduate student/course policies and procedures:  http://www.ugst.umd.edu/courserelatedpolicies.html