ma211: Linear Algebra I - w24
(CC BY-SA 4.0) : link
Class Meetings
- Winter 2024 (Jan16 → May4)
- MWF 11-11:50AM
- JXJ 3311
- zoom link - passcode 970032
Instructor
Daniel Rowe
darowe@nmu.edu
I'm an assistant professor of mathematics in the Mathematics and Computer Science Department at Northern Michgan University. I've been a professor at NMU for eight years, and I am very passionate about the praxis of doing mathematics and teaching it. I grew up on a fishing camp in Northwestern Ontario, Canada.
Need Math Help?
- Office Hours
- Tue 9-9:50AM, Thu 10-10:50AM, 1-1:50PM
- JXJ 2228
- zoom link - passcode 809390
- read the relevant section(s) of our materials
- study all posted solutions
- re-watch the recorded lectures
- math tutor lab
Success in College Classes
- the instructor's job is to ensure content is clear, organized, and engaging
- your job is to attend class, engage your mind, ask questions,
read the material, and apply yourself
Class Structure
- hybrid-flexible, in-person and over zoom
- recordings available 2-3 days after each class
- strive for in-person attendance
- avoid becoming reliant on zoom and recordings!
- use them for extenuating circumstances only
- engagement is vital to learning mathematics (or anything)
- I don't take daily attendance, but...
- overall attendance is 5% of your grade
- (35%) Homework
- (10%) Collaborative In-Class Quizzes
- (20%) Traditional In-Class Midterm Exam
- (30%) Traditional In-Class Final Exam
- (5%) Attendance
Grade Scale
A (92-100%)
A- (90-91%)
B+ (86-89%)
B (82-85%)
B- (80-81%)
C+ (76-79%)
C (72-75%)
C- (70-71%)
D+ (66-69%)
D (62-65%)
D- (60-61%)
F (≤ 59%)
Learning Outcomes
This is a course on the fundamentals of linear algebra. We will study matrices, matrix multiplication, and how to express linear systems via matrices. We consider the geometry of linear systems and then solve them via elementary matrices and echelon forms. Then we move on to vector spaces, subspaces, linear transformations, and the dimension formula. Finally we look at concepts related to a single linear operator: the determinant, conjugacy, eigenspaces, characteristic polynomials, and diagonalization. Throughout this course we will study various applications of linear algebra, for example, analyzing network flows, balancing chemical equations, calculating volumes, analyzing long term behaviour of markov processes, and solving recurrence relations.
Class Materials
Submitting Your Work
- for quizzes, midterm, final: physical paper in-class
- for homework: put a .pdf file inside our shared google folder
- the shared google folder will be titled w24_ma211_lastname
- I will share it with you within the first two weeks
- please don't submit anything via email attachment
- name your files in an organized manner, for example: hw1_Jane_Smith.pdf
- always show your work and keep it organized
- indicate/circle/highlight your answers
- answer the questions in the correct order
Late Submissions
- for quizzes, midterm, final: written in-class on the day
- for shared folder submissions: no late penalty until
the solutions are posted, then -50%
Checking Your Grade
- you can check your grade anytime, look for
untitled spreadsheet in our shared folder
Accessibility
If you have a need for disability-related accommodations or services, please inform the Coordinators of Disability Services in the Dean of Students Office at 2001 C. B. Hedgcock Building (227-1737 or disability@nmu.edu). Reasonable and effective accommodations and services will be provided to students if requests are made in a timely manner, with appropriate documentation, in accordance with federal, state, and University guidelines.
Extra Credit Problems
- list of extra credit problems
- (please read the instructions before you submit)
- repository of solved extra credit problems
- (check which problems have been solved before trying one)
Homework + Quizzes + Exams
Schedule + Recordings
wk1: jan15 → jan19
□ study this webpage and all class information
□ attend the lectures
□ start working on hw1
- 1/17
- announcements
- introduction to solving linear systems
- matrices
- 1/19
- matrix multiplication
- the meaning behind matrix multiplication
- geometry of vectors
wk2: jan22 → jan26
□ attend the lectures
□ keep working on hw1
- 1/22
- geometry of solution sets
- augmented matrix forms
- parametric vector form of solution sets
- 1/24
- 1 eq in 3 var = plane in R3
- 2 eq in 3 var = line in R3
- parametric vector form of solution sets
- help with hw1
wk3: jan29 → feb2
□ attend the lectures
□ start working on hw2
- 1/29
- elementary row operations
- intro to solving linear systems
- 1/31
- in-class collaborative quiz 1
- 2/2
- solving systems of equations
- reduced-row echelon forms (RREFs)
- the Gaussian Elimination process
wk4: feb5 → feb9
□ attend the lectures
□ keep working on hw2
- 2/5
- solving systems of equations
- examples
- 2/7
- solving systems of equations
- examples
- (# leading ones) vs. (dim solution set)
- 2/9
- bigger example: 3 eq, 5 var
- workshop on hw2
wk5: feb12 → feb16
□ attend the lectures
□ start working on hw3
- 2/12
- application #1: chemical equations
- application #2: network flow
- 2/14
- application #2: network flow
- application #3: curve fitting
- 2/16
- another network flow example
- application #4: families of systems
wk6: feb19 → feb23
□ attend the lectures
□ finish up hw3
- 2/19
- in-class collaborative quiz 2
- 2/21
- help with hw3
- abstract vector spaces
- 2/23
- abstract vector spaces
- span of vectors
wk7: feb26 → mar1
□ attend the lectures
□ work on hw4
- 2/26
- discussion of hw3
- independence/dependence
wk8: mar11 → mar15
□ attend the lectures
□ study for the midterm
□ finish up hw4
- 3/11
- a basis for a vector space
- nullspace of a matrix
wk9: mar18 → mar22
□ attend the lectures
□ midterm on monday
□ start working on hw5
- 3/18
- midterm exam (traditional, in-class, 11-11:50AM)
- 3/20
- subspaces
- finding the equation(s)
- 3/22
- finding the equation(s)
- elementary matrices
- intro to inverse matrices
wk10: mar25 → mar29
□ attend the lectures
□ work on hw5
- 3/25
- more on inverse matrices
- inverses of elementary matrices
- finding inverses in general
- 3/29
- example similar to quiz 3
- the rank-nullity theorem
wk11: apr1 → apr5
□ attend the lectures
□ finish up on hw5
□ start working on hw6
- 4/1
- determiants
- det via elementary matrices
- 4/5
- det via elementary matrices
- minors and cofactors
wk12: apr8 → apr12
□ attend the lectures
□ finish up hw5
□ start working on hw6
- 4/8
- det via cofactor expansion
- 4/12
- using the cross product
- intro to eigenvectors and eigenvalues
wk13: apr15 → apr19
□ attend the lectures
□ finish up hw5
□ start working on hw6
- 4/15
- eigenvectors and eigenvalues
- the characteristic polynomial
- 4/17
- multiplicities
- diagonalization
wk14: apr22 → apr26
□ attend the lectures
□ finish up hw6
□ study for the final exam
- 4/22
- application #1: markov chains
- application #2: recursive sequences
- 4/24
- application #2: recursive sequences
- help with hw6
wk15: apr29 → may3 (FINAL EXAM WEEK)
□ final exam: Mon Apr 29, 10-11:50AM, JXJ 3311
□ special office hour: Fri Apr 26, 2-3:00PM
□ traditional in-person exam
□ no electronic devices
□ complete any late homework for 50% (by 5/3 @ 11:59PM)
□ try an extra credit problem? (by 5/3 @ 11:59PM)
- class evaluations
- please fill out the class evaluation
- I would REALLY appreciate it!
- the evaluation link is active:
- now → Fri May 3 @ 11:59PM