Linear Algebra for Data Science: MAS 4115, Spring 2023 (2023)


Johnathan Bush (

time and place

Monday, Wednesday, Friday inSmall Room 233, Period 7 (1:55 pm-2:45 pm ET)

business hours

Wednesday, Friday at Small Hall 496, Hours 6 (12:50-1:40 pm ET) or by appointment.

From the course catalog:

Course Description

A second course in linear algebra that focuses on topics most relevant to data science. Introduces theory and numerical methods needed for large datasets and machine learning. Topics include LU, QR, and singular value decompositions; conditioning and stability; DFT and filters; deep learning; fully connected and convolutional meshes.


(MAS3114 or MAS4105) and MAC2313.

Specific to our section:

programming requirements

  • Class demos, examples, and homework use Python. Youthey are notYou are expected to have some prior knowledge of Python programming at the start of the course. on the other hand youit isIt is expected that you have enough programming experience to quickly learn the fundamentals of Python.
  • You don't need to have a laptop, though.What ifIf you have a laptop, please bring it to class.Most of our meetings include time to work on demonstrations and exercises, and you will make the most of our time together if you can actively participate. (If you don't have a laptop, I encourage people to share screens and collaborate.)
  • The first few weeks of the course are designed to help you learn the fundamentals of Python. We'll go through the basic syntax and functions. we are going to useGoogle Coand Jupyter notebooks, so you don't have to set up a complicated programming environment.

Course Objectives and Goals

A student who successfully completes this course will be able to:

  • Map data analysis problems to linear algebra concepts.
  • Perform basic linear algebra calculations manually and in Python.
  • Understand and implement various standard matrix decompositions and
    use its numerical implementation to analyze data and solve linear problems.
  • Build simple feedforward neural networks using learning functions, loss functions, and
    stochastic gradient descent.
  • Clearly discuss and explain mathematical concepts in the context of data science.

Temporary schedule:

  • Week 1-2: Basic linear algebra review: basic definitions, linear independence, basis, dimension, matrices, linear transformations, subspaces. Introduction to Python. Data as a high-dimensional vector space.
  • Week 3-4: Systems of equations, LU decomposition. More Python and libraries (focus on NumPy).
  • Week 5-6: inner products, orthogonality, norms; Clustering, non-linear dimension reduction (focus on tSNE), gradient descent.
  • Week 7-10: eigenvalues, eigenvectors, singular value decomposition, principal component analysis; Problems and techniques based on these concepts (linear dimensionality reduction, low-level approximations, etc.).
  • Week 11-14: Different neural networks, backpropagation, different loss functions, elements of information theory. Introduction to the Keras library.
  • Week 15: Breakout, recap.

Keep in mind that the schedule may need to be adjusted slightly during the semester to match the pace of our discussion.

Tasks and exams:

  • Homework.Homework will be posted on the screen.Most tasks contain some exercises that require basic programming.The lowest homework score is discarded.
  • written project.At the end of the semester, a longer project will be assigned. The objective is to research a topic of your choice using tools learned in class and put your observations in writing.
  • Exams:There are two intermediate exams and a final exam. These are traditional paper-and-pencil exams that are done without the use of technology. Exams serve to check your understanding of the theoretical basis of our methods.
  • Activity and Participation:I will encourage discussion and participation during classes. Most meetings include time to work on demonstrations and exercises, so you'll have ample opportunity to participate.

final notes:

Assessment is based on homework (40%), written project (10%), exams (40%) and activity and participation (10%). Final grades are assigned on a scale no more rigorous than the following: 93-100 A, 90-92 A-, 87-89 B+, 83-86 B, 80-82 B-, 77-79 C+, 73- 76C, 70-72C-, 67-69D+, 63-66D, 60-62D-, 0-59E.


Of course, you can use the Internet to look up Python definitions and documentation. You are also encouraged to work on assignments with other students, howeverYou must write and submit your own solutions/code.In addition, you must follow the guidelines below regarding Approved Assistance and let me know if you have any questions.

In this course, authorized assignment help is to talk to me, talk to other students, read your computing platform documentation, and review the text-based notes/demos/resources for this course. Therefore, unauthorized assistance includes, for example, reading solutions to problems online (or elsewhere), submitting work that is not yours, etc. See the Academic Honesty section below for more details.

Text-based features:

This course is largely based on notes and demonstrations. We won't be following a textbook through the semester, but here are some resources you might find helpful:

Additional information:


Attendance is mandatory. We will adhere to the University's attendance policy, which can be found here:

Grading points and grading guidelines:

We will follow the College's assessment guidelines, which can be found here:

Diversity Statement:

The University of Florida and Department of Mathematics are committed to diversity
and inclusion of all students. We recognize the diversity of our students' backgrounds and learning needs and strive to create a more inclusive and welcoming environment for all. We strongly believe that an inclusive learning environment encourages higher academic achievement.

Declaration of Disability:

Disabled students who encounter learning barriers and wish to apply for academic accommodation should contact the Disability Resource Center by visiting It is important that students share their housing letter with their professor and discuss their access needs as early in the semester as possible.

Course rating:

Students are expected to provide professional and respectful feedback on the quality of instruction in this course by completing online course evaluations through GatorEvals.
For instructions on how to provide feedback in a professional and respectful manner, visit will be notified when the assessment period begins and will be able to complete assessments via the email they receive from GatorEvals in the Canvas course menu on GatorEvals or via of course evaluation results are available to students at

Academic Honesty:

University of Florida students are bound by The Honor Pledge, which states: “As members of the University of Florida community, we are committed to holding ourselves and our fellow students to the highest standards of honor and integrity, promoting ourselves compliance with the honor code.” All work submitted for credit by University of Florida students will require or imply the following commitment: “On my honor, I have not given or received unauthorized assistance in the performance of this assignment. “The Code of Honor ( establishes a list of behaviors that violate this Code and possible sanctions. If you have any questions or concerns, please contact the instructor.

Campus resources:

  • Health and wellness:
    • You matter, we care: If you or someone you know needs it, get in touch, 352-392-1575, ou visite U Matter, We Care em escalate or report a concern and a member of staff will contact the student in need.
    • Counseling and wellness center: Visit the Counseling and Wellness Center website at call 352-392-1575 for information on crisis and non-crisis services.
    • Student Health Center: Call 352-392-1161 for 24-hour information to help you find the care you need, or visit the Student Health Care Center website at
    • University Police Department: Visit the UF Police Department website at call 352-392-1111 (or 9-1-1 for emergencies).
    • UF Health Shands Emergency Department/Trauma Center: For immediate medical attention, call 352-733-0111 or go to the emergency room at 1515 SW Archer Road, Gainesville, FL 32608; Visit the UF Emergency Room and Trauma Center website at
    • GatorWell Health Promotion Services: For prevention services focused on optimal wellness, including wellness training for academic success, visit the GatorWell website at call 352-273-4450.
  • Academic Resources:
    • Career Resource Center: Reitz Union, 352-392-1601, Career Assistance and Advice.
    • library stand: Different ways to get help using libraries or finding resources.
    • education Center: Broward Hall, 352-392-2010, 352-392-6420 ou General study and tutoring skills.
    • writing studio: 302 Tigert Hall, 352-846-1138, Help you brainstorm, format, and write articles.


Do I need to learn linear algebra for data science? ›

Linear algebra is an essential tool in data science and machine learning. Thus, beginners interested in data science must familiarize themselves with essential concepts in linear algebra.

How much linear algebra is used in data science? ›

As a mathematics-intensive domain, data science applies linear algebra techniques to transform and manipulate data sets effectively. In particular, data scientists use linear algebra for applications like vectorized code and dimensionality reduction, among others.

What is rank of a matrix in data science? ›

The rank of a matrix is the number of non-zero rows in the row echelon form of a matrix. So for the augmented matrix corresponding to the system of linear equations, the rank is 3.

Where can I learn linear algebra for data science? ›

Best Linear Algebra Courses for Data Science and Machine Learning
  • Linear Algebra Refresher Course– Udacity. ...
  • Mathematics for Machine Learning: Linear Algebra– Coursera. ...
  • The Math of Data Science: Linear Algebra– edX. ...
  • Learn Linear Algebra-Khan Academy. ...
  • First Steps in Linear Algebra for Machine Learning– Coursera.

Is linear algebra harder then calculus? ›

Calculus 3 or Multivariable Calculus is the hardest mathematics course. Calculus is the hardest mathematics subject and only a small percentage of students reach Calculus in high school or anywhere else. Linear algebra is a part of abstract algebra in vector space.

Is linear algebra too hard? ›

Many students regard linear algebra as a difficult study. It is more challenging than discrete mathematics which is usually a first-year program taught in most STEM majors. Linear algebra is taught in its second year and demands robust reasoning and analytical skills.

How many people pass linear algebra? ›

Linear algebra 1 - about 45% fail rate.

Is data science a lot of math? ›

Data science careers require mathematical study because machine learning algorithms, and performing analyses and discovering insights from data require math. While math will not be the only requirement for your educational and career path in data science, but it's often one of the most important.

Is linear algebra needed for coding? ›

Machine learning algorithms also rely heavily on linear algebra. While coders from other disciplines such as web development and front end development don't need to be linear algebra whizzes, understanding the concepts will help you find and use the right tools for advanced problem solving.

What are rank 1 matrices? ›

Rank one matrices

The rank of a matrix is the dimension of its column (or row) space. The matrix. 1 4 5 A = 2 8 10 2 Page 3 has rank 1 because each of its columns is a multiple of the first column.

Is my matrix full rank? ›

A matrix is full row rank when each of the rows of the matrix are linearly independent and full column rank when each of the columns of the matrix are linearly independent. For a square matrix these two concepts are equivalent and we say the matrix is full rank if all rows and columns are linearly independent.

Can a matrix have rank 4? ›

Sure, you can have a matrix of rank 4, or 5 or 6 or any higher integer. It's just you need longer vectors, spaces of higher dimension than 3 (indeed the Cliff's notes explicitly state 3-vectors).

Is linear algebra higher than calculus? ›

Linear Algebra- At the lower division level, this isn't really more advanced than calculus. You start off learning about vectors and matrices and their properties and some useful things you can do with them.

What grade do you learn linear algebra in? ›

Linear algebra is standard topic in the college mathematics curricula. It is usually taken by students in their sophomore year. Linear Algebra is required for math, physics, engineering, statistics, and economics majors.

Is it worth learning linear algebra? ›

You must learn linear algebra in order to be able to learn statistics. Especially multivariate statistics. Statistics and data analysis are another pillar field of mathematics to support machine learning. They are primarily concerned with describing and understanding data.

Which math class is hardest? ›

What is the Hardest Math Class in High School? In most cases, you'll find that AP Calculus BC or IB Math HL is the most difficult math course your school offers. Note that AP Calculus BC covers the material in AP Calculus AB but also continues the curriculum, addressing more challenging and advanced concepts.

Which is harder Calc 2 or linear algebra? ›

Linear Algebra from a textbook with traditional lectures can be challenging. Many students in traditional lecture courses do rate Linear Algebra as a more difficult course than Calculus I and Calculus II.

Is linear algebra the hardest math? ›

Is linear algebra the hardest math class? No, linear algebra is not the hardest, there are another maths harder then linear algebra.

How much time do I need to learn linear algebra? ›

It really took some time for me to grasp the concepts, especially the matrix/linear transformating correlation. I strongly suggest to take more time for that. I learned introductory linear algebra over the course of about 2 months and that was studying it for at least 5 or 6 hours every day.

What math is harder than calculus? ›

At an advanced level, statistics is considered harder than calculus, but beginner-level statistics is much easier than beginner calculus. Frankly, it mostly depends upon the student's interest as some students find it hard to comprehend statistics while others find it hard to understand calculus.

Is linear algebra or statistics harder? ›

Statistics requires a lot more memorization and a deeper level of analysis/inference skills while algebra requires little memorization and very little analysis outside of algebraic applications.

Is linear algebra harder than calculus 3? ›

I found Linear Algebra to be the most difficult because it's more abstract then any other math course I had to take for my Engineering Physics curriculum and you really need to understand everything about it and it's abstractness in order to succeed in that course.

Why do so many students fail algebra? ›

Algebra is overwhelming for many students because it's the first math class they take where they must wrestle with variables, abstract concepts, and creative problem solving. And there's often not enough done in the classroom to connect Algebra to their everyday lives and explain why it's worth understanding.

What is the failure rate of college algebra? ›

Research from the National Center for Education Statistics reveals 51% of students in remedial algebra classes at two-year schools and 41% at four-year schools never earn a passing grade.

Can I do data science if I'm bad at math? ›

First of all, can you actually break into data science without a background in math or STEM? The answer is yes! While data science requires a strong knowledge of math, the important data science math skills can be learned — even if you don't think you're math-minded or have struggled with math in the past.

Is an average student become data scientist? ›

If you have strong knowledge of algorithms, you can easily build data processing models. However, even if you don't have strong coding knowledge and a special degree in data science, you can still become a data scientist. With good learning capability, you can be a data scientist without a degree in it.

Can I be a data analyst if I'm bad at math? ›

While data analysts need to be good with numbers, and a foundational knowledge of Math and Statistics can be helpful, much of data analysis is just following a set of logical steps. As such, people can succeed in this domain without much mathematical knowledge.

Should I learn linear algebra or calculus first? ›

Areas of mathematics such as statistics and calculus require prior knowledge of linear algebra, which will help you understand ML in depth.

Is linear algebra The most important math? ›

Introduction to Linear Algebra Basics

Linear algebra is also central to almost all areas of mathematics like geometry and functional analysis. Its concepts are a crucial prerequisite for understanding the theory behind machine learning, especially if you are working with deep learning algorithms.

Can I learn linear algebra without knowing algebra? ›

Linear algebra is such a general concept, which permeates almost everything in mathematics, that it can be studied at any level, even though it is may not be called linear algebra at that level.

Is there a rank 0 matrix? ›

The zero matrix is the only matrix whose rank is 0.

What rank 1 means? ›

idiom. : being excellent at what one does.

What does a rank 0 matrix mean? ›

The rank of a null matrix is zero. A null matrix has no non-zero rows or columns. So, there are no independent rows or columns. Hence the rank of a null matrix is zero.

What grade level is matrix? ›

Elementary matrix (kindergarten through 5th) Secondary matrix (6th grade through calculus)

What is the easiest way to find the rank of a matrix? ›

The rank of a matrix is equal to the number of linearly independent rows (or columns) in it. Hence, it cannot more than its number of rows and columns. For example, if we consider the identity matrix of order 3 × 3, all its rows (or columns) are linearly independent and hence its rank is 3.

What happens if a matrix is not full rank? ›

One dimension is lost during linear transformation if matrix is not full rank by definition. This implies determinant will be 0 and that some information is lost in this linear transformation.

Can a 3x3 matrix have rank 3? ›

Recall that the rank of a matrix 𝐴 is equal to the number of rows/columns of the largest square submatrix of 𝐴 that has a nonzero determinant. Since this is a 3 × 3 matrix, its rank must be between 0 and 3.

What does rank 2 mean in matrix? ›

Linear Algebra

The fact that the vectors r 3 and r 4 can be written as linear combinations of the other two ( r 1 and r 2, which are independent) means that the maximum number of independent rows is 2. Thus, the row rank—and therefore the rank—of this matrix is 2.

What is eigen value of a matrix? ›

The eigenvalue is explained to be a scalar associated with a linear set of equations which, when multiplied by a nonzero vector, equals to the vector obtained by transformation operating on the vector. Here, λ is considered to be the eigenvalue of matrix A. Where “I” is the identity matrix of the same order as A.

What is the highest math level? ›

Typical Math Progression
  • Arithmetic (grades k-8)
  • Pre Algebra (grades 6-9)
  • Algebra 1 (grades 8-10)
  • Geometry (grades 9-10)*
  • Algebra 2 (grades 10-12)
  • Trigonometry / Pre-Calculus (grades 10-12)
  • Calculus (grades 10-12)
Mar 11, 2022

What math comes after linear algebra? ›

If you are a math major:

As an entering student, you will probably go into Calculus II, then Linear Algebra, followed by Calculus III.

What is the highest math class in high school? ›

Therefore, according to the Common Core standards, a typical order of core High School Math curriculum from freshman to senior year is:
  • Algebra 1.
  • Geometry.
  • Algebra 2/Trigonometry.
  • Pre-Calculus.
  • Calculus.
Mar 1, 2021

Is linear algebra a college level? ›

Course Overview

Due to its broad range of applications, linear algebra is one of the most widely taught subjects in college-level mathematics (and increasingly in high school).

Is Linear Algebra high level math? ›

Linear algebra is usually taken by sophomore math majors after they finish their calculus classes, but you don't need a lot of calculus in order to do it.

What math do I need to know before linear algebra? ›

So, for those students wishing to get ahead and get Linear Algebra in their completed column in their academic plan, you do need to complete Calculus II first, which means also completing Calculus I first, even though Linear Algebra has nothing to do with either course.

Why is linear algebra so powerful? ›

Linear algebra is vital in multiple areas of science in general. Because linear equations are so easy to solve, practically every area of modern science contains models where equations are approximated by linear equations (using Taylor expansion arguments) and solving for the system helps the theory develop.

Do you need linear algebra for AI? ›

Linear Algebra You Need to Know for AI

Source. Linear Algebra is the primary mathematical computation tool in Artificial Intelligence and in many other areas of Science and Engineering.

Do software engineers need linear algebra? ›

Yes. If you look at a list of required coursework for a degree in software engineering, you'll typically see Calculus I-III, Differential Equations, Discrete Mathematics, Linear Algebra, and other advanced math classes.

Does data science use linear algebra or calculus? ›

Then we help you find a job and start your career. If you're doing data science, your computer is going to be using linear algebra to perform many of the required calculations efficiently. If you perform a Principal Component Analysis to reduce the dimensionality of your data, you'll be using linear algebra.

What math do you need for data science? ›

How much math is needed in the field of data science? A wide range of mathematical concepts is put into play. But if you're starting from scratch, you should focus your studies on three core areas, the so-called Big Three. This includes: Linear algebra, calculus, and most importantly, statistics and probability.

Can I do data science if im not good at math? ›

Data science careers require mathematical study because machine learning algorithms, and performing analyses and discovering insights from data require math. While math will not be the only requirement for your educational and career path in data science, but it's often one of the most important.

Do data analysts use linear algebra? ›

Algebra. College-level algebra is frequently used in data analytics. In particular, linear algebra is necessary for any professional who aims to work with machine learning and/or AI, as most algorithms make use of it.

Which is harder linear algebra or discrete math? ›

I think discrete math is harder than calculus or linear algebra, but that may be a personal thing. Discrete math covers a diverse number of topics which have their own particular methods, whereas calculus relies on a handful of tricks which you can apply over and over again.

Is data science more math or coding? ›

Data science is basically statistics, calculus linear algebra put together. Programming is just a way to automate those mathematical calculations which a human would take years do. So yes, Math is at the heart of data science and you need to be strong at Mathematics to understand data science.

Is math in data science hard? ›

Data science is a difficult field. There are many reasons for this, but the most important one is that it requires a broad set of skills and knowledge. The core elements of data science are math, statistics, and computer science. The math side includes linear algebra, probability theory, and statistics theory.

How can I get better at math for data science? ›

One of the best ways to learn math for data science and machine learning is to build a simple neural network from scratch. You'll use linear algebra to represent the network and calculus to optimize it. Specifically, you'll code up gradient descent from scratch.

How much calculus is needed for data science? ›

Data Science doesn't actually require much calculus, other than as a prerequisite to probability and statistical theory. Linear Algebra, as it is the basis of modern practical computing. Least squares, dimensionality reduction, collinearity, and more, all can be understood in terms of Linear Algebra.

Can a average student can do data science? ›

If you have strong knowledge of algorithms, you can easily build data processing models. However, even if you don't have strong coding knowledge and a special degree in data science, you can still become a data scientist. With good learning capability, you can be a data scientist without a degree in it.

Is data science a difficult degree? ›

No, if one has learned the right set of skills, data science will not be a hard job for them. The field of data science is new and has not matured fully yet. So it might seem difficult when you start. But once you learn the nuts and bolts of it, it is not a hard job.

Can a non IT student do data science? ›

Data Science is only for persons with an IT background. It is a persistent myth that many people believe. Although it is true that some IT professionals seek to advance their skills in analytics, this field is not only open to people with a background in programming and IT.

Is linear algebra like calculus? ›

No, Linear Algebra turns out to be a completely different subject than is Calculus 2. So why is Calculus 2 the prerequisite? In Math Education, the reason is explained as to requiring a "mathematical maturity" of the student enrolling in Linear Algebra.

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