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.

You may download it for your personal use only.

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.

Grading Policy: Homework grade 20%, Midterm grade 40%, Final exam 40%. A plus/minus system will be used in reporting the final grades.

Homework: Homework must be typed or written in ink. All homework problems will be taken from the exercises in the text and will be assigned in the Assignments section of Zoom and/or on the web at Homework, Midterms, and Exam with a specified due date. It  must be uploaded via Zoom bu midnight.

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.

Students missing a test or exam will receive a grade of zero unless they have requested and received from me in writing an approved absence. For students with an approved absence the term test component of the final grade will be computed from the other two test grades. 

Approvals will normally be granted only in the following circumstances: religious observances; mandatory military obligations; serious family or medical issues; or conflicts with other university requirements.  

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 Schedule:      Midterm 1: Fri. Feb. 21 in class

                                      Midterm 2: Fri. Apr. 10  NOTE Change !!

                                      Midterm 3: Fri. May 1 

                               
Final exam: 

       Time and Date (Tentative) Mon May 18, 8 AM-10 AM

       Location: TBD

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.

You may download it for your personal use only.

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.

Grading Policy: Homework grade 20%, Midterm grade 40%, Final exam 40%. A plus/minus system will be used in reporting the final grades.

Homework: Homework must be typed or written in ink. All homework problems will be taken from the exercises in the text and will be assigned in the Assignments section of Zoom and/or on the web at Homework, Midterms, and Exam with a specified due date. It  must be uploaded via Zoom bu midnight.

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.

Students missing a test or exam will receive a grade of zero unless they have requested and received from me in writing an approved absence. For students with an approved absence the term test component of the final grade will be computed from the other two test grades. 

Approvals will normally be granted only in the following circumstances: religious observances; mandatory military obligations; serious family or medical issues; or conflicts with other university requirements.  

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 Schedule:      Midterm 1: Fri. Feb. 21 in class

                                      Midterm 2: Fri. Apr. 10  NOTE Change !!

                                      Midterm 3: Fri. May 1 

                               
Final exam: 

       Time and Date (Tentative) Mon May 18, 8 AM-10 AM

       Location: TBD

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