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README.md

README.md

Math 317: Linear Algebra, Spring 2016

Instructor: Dr. William DeMeo
Email: [williamdemeo at gmail](mailto:williamdemeo@gmail.com?subject=MATH 317: (insert an informative subject))
Office: Carver 466.
Office hours: Mon, Tue, Thu 2:10--3pm.
Lecture time and location: Mon, Tue, Thu, Fri 1:10--2pm, Carver 0132.


Course Webpage: http://github.com/williamdemeo/Math317-Spring2016

Piazza: https://piazza.com/iastate/spring2016/math317

Number of Credits: 4


Remarks about office hours: The regularly scheduled office hours listed above are subject to change. Changes will be announced during lecture. It is helpful (but not required) to send me an email in advance to let me know when you plan to visit.


Table of Contents


Introduction

You are now reading the main course web page. The paragraphs below serve as the syllabus for Math 317 Section A.

This page, as well as the content directory above, and its subdirectories, will be updated throughout the semester. Students are expected to visit this page periodically.

Please bookmark this page or, better yet, click here to email the url of this page to yourself!

The ISU Blackboard system will be used only for recording test scores and grades. Please Note, the Blackboard system often reports cumulative grade totals that bear little relation to the course grades as they will be computed at the end of the semester. If you want to find out where you stand in the class, please keep track of your grades and refer to the Grading Policy section below.

Class Meeting Times

Lecture: MTTF 1:10--2pm Carver 0132

Overview, Prerequisites, Outcomes

Overview

This course emphasizes the reading and writing of mathematical proofs realted to linear algebra. We will cover chapters most of Chapters 1 through 6 of the textbook. Some topics covered are the following:

  • Vectors, matrices, linear equations;
  • Matrix algebra;
  • Vector spaces;
  • Projections, linear transformations, determinants;
  • Eigenvalues, eigenvectors;
  • Some applications if time permits.

Prerequisites

Math 165, Math 166 or equivalent, Math 201 at the same time or earlier; Math 265 also is suggested.

Learning Outcomes

Students will gain proficiency in reading and writing proofs, as well as solving computational problems, concerning the following topics: systems of linear equations, determinants, vector spaces, inner product spaces, linear transformations, eigenvalues and eigenvectors, diagonalization of linear transformations.

See the list of Course Objectives below for more details.

Textbook Information

Title: Linear Algebra
Author: Shifrin and Adams
Edition: 2nd
ISBN: 9781429215213

It is helpful (but not mandatory) to have a hard copy of the textbook. Students should at least have access to an electronic version of the book by Shifrin, or a comparable linear algebra book. It may be possible for some students to get by with just the lecture notes, but that is not recommended.

The textbook for this class is very expensive when purchased at the university bookstore. Students are free to purchase the book from alternative sources. (At last check, some Amazon merchants are listing new editions of the book for around $80). Please note: shipping delays or other problems that may arrise when trying to find a cheaper copy of the textbook do not constitute a valid excuse for failing to submit homework on time.

Exams

There will be two midterm exams each worth 20%, and a final exam worth 30% of the course grade.

  • MIDTERM EXAM 1 (focus on Chapters 1 and 2)
    DATE: Friday, February 19 (subject to change)

  • MIDTERM EXAM 2 (focus on Chapters 3 and 4)
    DATE: Monday, April 4 (subject to change)

  • FINAL EXAM (focus on Chapters 1--6 and Section 7.1)
    DATE: Monday, May 2, 2016
    TIME: 12--2pm
    LOCATION: Carver 0132

The final exam will be cumulative, that is, it will cover everything we have learned during the semester.

In accordance with university policy, the final exam is mandatory and must be taken by all students at the scheduled time. Do not make travel plans before the date of the final exam.

Homework

Late homework will not be accepted or graded.

Solving lots of problems is the best way to prepare yourself to do well on the tests, and ultimately to do well in the course.

The homework will account for 25% of the course grade and will be assigned once per week, typically due each Friday at the beginning of class. You must submit a hard copy of your homework. Electronic documents (e.g., email attachments) are not acceptable.

Homework submitted at the end of class on the due date will be penalized 10%. Homework submitted after then end of class on the due date will not be accepted or graded.

At least one (possibly more) of the lowest or missed homework scores will be dropped and not counted toward the final course grade. The 10 best homework scores will count toward the final grade.

The last homework assignment will be due during the last week of the semester, also known as "dead week."

Computer Lab

Four of the Friday class meetings will be held in the Computer Lab on the fourth floor of Carver in Room 449. Specifically, we will meet in the Computer Lab (instead of our usual classroom) on the following dates:

January 29, February 12, March 25, April 15

The Computer Lab component is worth 5% of the final course grade.

Students are required to show up for each computer lab, login to a computer, and register for (or sign-in to) an account on the Math Department's Sage server. Doing so earns the student one percentage point (per lab). Students can then earn one additional point (per lab) by completing that day's lab assignment during that day's lab period (from 1:10 to 2pm). Lab assignments must be completed on the day they are assigned. No late lab assignments will be accepted.

Thus, there is a total of 8 Computer Lab points available over the course of the semester. Since the computer lab component accounts for just 5% of the course grade, this means there is a possibility of earning 3 extra credit points by completing all of the Computer Lab assignments. On the other hand, if a student merely shows up to each Computer Lab session and signs on to their account, but does not complete any of the computer assignments, then that student will earn 4 out of 5% for this component of the course grade.

Make-up Policy

No late homework will be accepted for any reason. If you fail to submit homework on time, this will not necessarily hurt your course grade since the lowest homework scores will be dropped.

Generally speaking, there are no make-up exams. However, if you must miss an exam for one of the legitimate reasons listed below, and if you contact the professor at least five days before the exam date, then you might be able to take a make-up exam before the scheduled exam time.

To request a make-up exam, a student must provide documented evidence of one of the following:

  • Medical excuse - student's own medical emergency.
  • Medical excuse - a member of the student's family has a medical emergency.
  • Extra curricular activities as a representative of Iowa State University.
  • Armed forces deployment (military duty).
  • Officially mandated court appearances, including jury duty.
  • A conflict with another exam or if you have three or more final exams on a given day. (In each case the exam with the fewest students must arrange the make-up exam.)

If you miss an exam due to some unforeseen circumstance, you must contact the professor within one class meeting after the missed test and provide an explanation. If your excuse is accepted, the missed test score may be replaced with 80% of your final exam score. For example, if your excuse is accepted and you score a 90% on the final, then you will receive a 72% for the missed test (0.80*0.90 = 0.72).

Grading Policy

The breakdown of the final course grade is as follows:

  • Final exam: 30 points
  • Mid-term exams: 40 points (20 each)
  • Homework: 25 points total
  • Computer Lab: 5 points total

At the end of the semester, letter grades will be assigned roughly according to the following table. However, the scale may be shifted, depending on overall student performance. All curving (if any) will occur at the end of the semester.

  • A: 94--100
  • A-: 91--93
  • B+: 87--90
  • B: 84--86
  • B-: 81--83
  • C+: 77--80
  • C: 74--76
  • C-: 71--73
  • D+: 67--70
  • D: 64--66
  • D-: 60--63
  • F: 0--59

Attendance

Students are expected to attend all classes. A grade penalty will be exacted if you have an excessive number of absences (whether excused or unexcused). Specifically, you are permitted (but strongly discouraged from taking) seven absences in total, and you must email the instructor if/when you must miss a class. Each additional absence, and any absence not mentioned to the instructor, may result in the deduction of points from your final grade.

Occasionally attendance will be recorded by passing around a sign-in sheet on which you will print and sign your own name. If another student asks you to sign in for them, don't do it! Forging another student's signature constitutes a violation of the student code of conduct and will be referred to the ISU Office of Judicial Affairs.

Important: If you plan to leave before class is over, the correct procedure is to mention this to the professor before the start of class. It is impolite and disruptive to your classmates to leave, or even pack up your belongings, before the lecture is over.

Asking Questions

When you don't understand something, please ask a question!

  1. In Lecture. The best time/place to ask a question is during lecture or recitation or office hours.

  2. On Piazza. Another good place to ask a question is the online discussion forum. This term we will be using Piazza for class discussion and all students should enroll in this forum by visiting the Piazza signup page.

    This system is highly catered to getting you help fast and efficiently from classmates, the TA, and the professor. Rather than emailing questions to the teaching staff, students are encouraged to post questions on Piazza forum. If you have any problems or feedback for the developers, email team@piazza.com.

    Our class Piazza page is at: https://piazza.com/iastate/spring2016/math317/home

Email Policy

You may email the instructor directly, though the response time will generally be slower than if you use one of the preferred methods described above.

If you email the instructor, you must use an informative subject field. If you use this link to email the professor, then some of the required information should pre-populate your message fields. If you do not at least indicate which class you are in, your email may be ignored.

Use of Electronics During Lecture

Silence and refrain from using all electronic devices (phones, ipods, tablets, microwave ovens, etc.) during class and exam periods. Using a computer during lecture to check Facebook, for example, is totally unacceptable. Besides how this affects your own ability to focus on what is being taught in the lecture, computers can be very distracting to other students. Use of electronic devices in lecture for purposes unrelated to math will not be tolerated.

Academic Honesty

Cheating is unacceptable and will not be tolerated. Violations of this policy will be referred to and dealt with by the ISU Office of Judicial Affairs, in a manner consistent with university regulations, which range from a warning to expulsion from the university.

Classroom Policy

In this course, we follow the general university classroom policy: http://www.math.iastate.edu/Faculty/ClassPolicies.html

Students With Disabilities

If you have a documented disability or if you believe that you have a disability that qualifies under the Americans with Disabilities Act and Section 504 of the Rehabilitation Act and requires accommodations, you should contact the Student Disability Resources Office for information on appropriate policies and procedures.

The Disability Resources Office
Student Services Building, Room 1076
phone: 515-294-6624, or 515-294-7220, or TDD 294-6335
email: disabilityresources@iastate.edu or accommodations@iastate.edu.

You must obtain a Student Academic Accommodation Request (SAAR) from the Disability Resources office and you must contact your instructor early in the semester so that your learning needs may be appropriately met.

Your instructor will be happy to assist with accommodations, but will not provide them retroactively, so the appropriate requests and paperwork should be filed well before the first exam.

More information about disability resources in the Mathematics Department can be found at http://www.math.iastate.edu/Undergrad/AccommodationPol.html.


Course Objectives

  • Be able to reduce a matrix to row canonical form and solve the system of linear equations Ax = B.
  • Be able to prove that the row canonical form of a matrix is unique.
  • Know the Elementary row operation matrices and use them in proofs.
  • Know the algebraic operations of matrices and proof of associativity.
  • Know the characteristic polynomial, the relationship between the roots of the characteristic polynomial and the minimal polynomial. Know the relationship between these roots and the blocks of the Jordan Canonical Form.
  • Know diagonalization of matrices and the theorems about its existance.
  • Understand the definitions of linear independence and spanning and be able to prove every spanning set can be reduced to a basis and any independent set can be augmented to a basis.
  • Know the definition of a determinant as the signed volume of an ordered simplex. and be able to prove the basic properties of the determinants from this definition, including Det[AB] = Det[A] Det[B].
  • Know the definition of a linear transformation and be able to set up the matrix of a linear transformation on a finite dimensional vector space.
  • Know the definition of an eigenvalue and an eigenvector and be able to compute then for low dimension matrices.
  • Know the basic properties of the dot product and how to compute distances from points to planes, points to lines, angles between planes, angles between lines. Know the basic 3 dimensional constructions and their generalizations to higher dimensions including the distance formula.
  • Know unit vectors and their uses in projections.

Additional Resources

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