Mathematics 233 :  Linear Algebra I
  Fall 2025

Introduction

Professor:          Jeff Johannes                                 Section 2    MWF  1:30-2:20p    South 328
Office:               South 326A                                
Telephone:         5403 (245-5403)                                                            
Office Hours Open Classroom Time with Jeff: Monday 2:30 - 3:20p (South 328), Tuesday 10:30 - 11:20a (Fraser 116), Wednesday 2:30 - 3:20p (South 328), Thursday 11:30a - 12:30p (South 328) and 8-9p (South 336). 
Email Address:  Johannes@Geneseo.edu
Web-page:          http://www.geneseo.edu/~johannes

Course Materials

    Primary:  Activity Workbook for Understanding Linear Algebra, by D. Austin
   
Support:  Understanding Linear Algebra, by D. Austin

Purposes

Overview

    Linear algebra is the algebra of anything resembling straight lines.  And since lines were the first algebraic objects you studied, this can't be bad, right?  Well, yes and no.  Linear algebra is based on the most basic of algebraic fundamentals.  And then planes are like lines.  And lines in three dimensions are like lines in two dimensions.  But they're a little more complicated.  And away we go.  Linear algebra is about the simplest geometry (linear) of higher dimensions.  Along the way we will also study vectors and matrices as valuable notation for working in different dimensions.  

Activities 

    Most days we will be working on scheduled activities from the workbook after a brief introduction to any necessary content from the text.  Almost all days have preview activities.  They are indicated by * in the schedule.  Expect that they are there and if you find a day without one, you can celebrate.  On other days, I do not expect you to read the text or the activities before class.  Previewing them before class could help, but please do not complete the main activities before class. 

Learning Outcomes

Students will be able to:
    •    Solve systems of linear equations,
    •    Analyze vectors in R^n geometrically and algebraically,
    •    Recognize the concepts of the terms span, linear independence, basis, and dimension, and apply these concepts to various vector spaces and subspaces,
    •    Use matrix algebra and the related matrices to linear transformations,
    •    Compute and use determinants,
    •    Compute and use eigenvectors and eigenvalues,
    •    Determine and use orthogonality, and
    •    Use technological tools such as computer algebra systems or graphing calculators for visualization and calculation of linear algebra concepts.


Grading

    Your grade in this course will be based upon your performance on homework, quizzes and three exams.  The weight assigned to each is designated below:
        Problem Sets (6)          5% each
        Quizzes (3)                   5% each
        In-class exams (2)        15% each
        Final exam (1)              20%
        Something Else (1)       5%
        

Problem Sets

    There will be problem sets assigned at the beginning of the course.   Problem sets will be due shortly after each chapter ends.  You are encouraged to consult with me outside of class on any questions toward completing the problem sets.  You are also encouraged to work together on homework assignments, but each must write up their own well-written solutions.  A good rule for this is it is encouraged to speak to each other about the problem, but you should not read each other's solutions.  A violation of this policy will result in a zero for the entire assignment and reporting to the Dean of Students for a violation of academic integrity.  Each question will be counted in the following manner:
    0 – missing or plagiarised question
    1 – question copied
    2 – partial question
    3 – completed question (with some solution)
    4 – completed question correctly and well-written
Each entire problem set will then be graded on a 90-80-70-60% (decile) scale.  Late items will not be accepted, as solutions will be posted immediately.  Homework will be returned on the following class day.  Please feel free to discuss any homework with me outside of class or during review.   

Solutions and Plagiarism

    There are plenty of places that one can find all kinds of solutions to problems in this class.  Reading them and not referencing them in your work is plagiarism, and will be reported as an academic integrity violation.  Reading them and referencing them is not quite plagiarism, but does undermine the intent of the problems.  Therefore, if you reference solutions you will receive 0 points, but you will *not* be reported for an academic integrity violation.  Simply - please do not read any solutions for problems in this class. 

Opening Meeting

    Students will earn two extra points on the first problem set by visiting office hours during the first two weeks of classes, i.e. no later than 10 September. 

Quizzes

    There will be short quizzes after problem sets have been returned, covering the material from the problem set.  For problem sets immediately preceding exams, there will be no quiz.  Quizzes will consist of short pencil-paper computations, and will have limited opportunity for partial credit. Because quizzes will consist of routine questions, they will be graded on a decile scale. There will be no makeup quizzes.

Exams

    There will be two exams during the semester and a final exam during finals week.  If you must miss an exam, it is necessary that you contact me before the exam begins.  The final exam will be half an exam focused on the final third of the course, and half a cumulative exam.  Exams will be graded on a scale approximately (to be precisely determined by the content of each individual exam) given by
    100 – 80%   A
     79 – 60%    B
     59 – 40%    C
     39 – 20%    D
    below 20%   E
For your interpretive convenience, I will also give you an exam grade converted into the decile scale.  The exams will be challenging and will require thought and creativity.  They will not include filler questions (hence the full usage of the grading scale).

Something More

     No later than 15 September, you and I will mutually agree on something that you will include for the remaining 5% of your assessment.  The goal is that it is somehow relevant to our course and valuable to your learning.  I'm open to good ideas.

Feedback

    Occasionally you will be given anonymous feedback forms.  Please use them to share any thoughts or concerns for how the course is running.  Remember, the sooner you tell me your concerns, the more I can do about them.  I have also created a web-site which accepts anonymous comments.  If we have not yet discussed this in class, please encourage me to create a class code.  This site may also be accessed via our course page on a link entitled anonymous feedback.  Of course, you are always welcome to approach me outside of class to discuss these issues as well. 

Social Psychology

    Wrong answers are important.  We as individuals learn from mistakes, and as a class we learn from mistakes.  You may not enjoy being wrong, but it is valuable to the class as a whole - and to you personally.  We frequently will build correct answers through a sequence of mistakes.  I am more impressed with wrong answers in class than with correct answers on paper.  I may not say this often, but it is essential and true.  Think at all times - do things for reasons.  Your reasons are usually more interesting than your choices.  Be prepared to share your thoughts and ideas.  Perhaps most importantly "No, that's wrong." does not mean that your comment is not valuable or that you need to censor yourself.  Learn from the experience, and always try again.  Don't give up. 

Academic Dishonesty

    While working with one another is encouraged, all write-ups of assignments must be your own. You are expected to be able to explain any solution you give me if asked. Assignments and exams will be done individually. The Student Academic Dishonesty Policy and Procedures will be followed should incidents of academic dishonesty occur.  Any work written, developed, or created, in whole or in part, by generative artificial intelligence (AI) is considered plagiarism and will not be tolerated. While the ever-changing developments with AI will find their place in our workforces and personal lives, in the realm of education and learning, this kind of technology does not help us achieve our educational goals. The use of AI prevents the opportunity to learn from our experiences and from each other, to play with our creative freedoms, to problem-solve, and to contribute our ideas in authentic ways. Geneseo is a place for learning, and this class is specifically a space for learning how to advance our thinking and professional practice. AI cannot do that learning for us.

Math Learning Center

    This center is located in South Hall 332 and is always open, staffed with tutors during the day and some evenings. Hours for the center will be announced in class. The Math Learning Center provides free tutoring on a walk-in basis.

Accessibility Accommodations    

    SUNY Geneseo is dedicated to providing an equitable and inclusive educational experience for all students. The Office of Accessibility (OAS) will coordinate reasonable accommodations for persons with disabilities to ensure equal access to academic programs, activities, and services at Geneseo.  Students with approved accommodations may submit a semester request to renew their academic accommodations. Please visit the OAS website for information on the process for requesting academic accommodationsContact the OAS by email, phone, or in-person:  Office of Accessibility Services Erwin Hall 22 585-245-5112 access@geneseo.edu.

Religious Holidays

    It is my policy to give students who miss class because of observance of religious holidays the opportunity to make up missed work.  You are responsible for notifying me by September 8 of plans to observe a holiday.  

 

Schedule (subject to change)


Date              Topic                                                           
August 25     Introduction
        27          1.1
        29          1.2*
 
September 3  1.3
        5             1.4*                                                     

        8             2.1*
        10           2.2*
        12           2.3* PS 1 (1.1-1.4, 2.1) due

        15          2.4*  (Something More deadline)
        17          Q1 (1.1-1.4, 2.1) 2.5*                         
        19          2.6*                 
 
        22          overrun / 3.1*
        24          review PS2 (2.2-2.6) due                        
        26          review
 
        29          XM1 (1.1-2.6)
October 1      3.2*
        3                             

        6          3.3* (or push back if overrun needed)
        8          3.4* 
        10        3.5*             
                
        15          4.1*  PS3 (3.1-2,4-5) due
        17          4.2*

        20          Q3 (3.1-2,4-5) 4.3*
        22          4.4*                                                    
        24          overrun or 4.5*

        27         review   PS4 (4.1-3) due
        29         review     
        31         XM2 (3.1-2,4-5, 4.1-3)

November 3  6.1*
        5           6.2*
        7           6.3*

        10         6.4*
        12         overrun or 6.5                                                                                                                       
        14         VS.1 PS6 (6.1-4) due   
    
        17         VS.2
        19         Q6 (6.1-4) VS.3
        21         VS.4 

        24         VS.5

December 1    overrun
        3             overrun
        5             review PSVS (VS.1-5) due

       8            review

Wednesday, December 10 final exam (half 6 & VS, half 1-4) 12N - 2:30p