QRC Resource Directory
Quantitative Resource Center, Lawrence University. Version 0.7, updated 2026-10-10. Free, vetted resources for quantitative work. Entries marked ★ are QRC picks.
Short guides
Your first visit to the QRC
Drop-in tutoring is free. You don't need an appointment, and you don't need to have finished the assignment.
Before you come. Bring the problem, your notes, and the textbook or Canvas page it came from. If you can, try the problem first and mark where you got stuck. A half-finished page is fine. So is a blank one.
When you get there. Check the tutor board by the door to see who's on. Sign in, then tell the tutor your course and what you want to be able to do by the time you leave. Tutors often work with a few people at once, so you may start on your own for a few minutes.
What tutors do. They ask questions, work a similar example with you, and check your reasoning. They won't do graded work for you, and they follow your course's collaboration policy.
If drop-in isn't the right fit. To get a tutor for a specific course, request one through Course tutors through Navigate. For time management or study habits, meet with a coach at the Center for Academic Success.
Stuck on a problem? A 10-minute routine
Most "I don't get any of it" turns out to be one stuck step. This routine finds it.
The routine
- Write what the problem asks for in your own words.
- List what you know: the given values, plus the definitions and formulas from this section.
- Find the exact step where you stall. Is it a definition, choosing a method, the algebra, or reading the problem?
- Find a worked example of that step in your textbook or in Paul's Online Math Notes. Copy it out by hand, then try yours again.
- Check your answer: units, sign, a rough estimate, or a quick graph in Desmos graphing calculator.
- Still stuck after 10 minutes? Bring what you wrote to the QRC. Your notes from steps 1–3 make a tutor's job much faster.
Studying for a math exam in 10 days
Cramming feels productive and isn't. Short, mixed practice spread over a week and a half works better.
10 days out. List every topic on the exam from the syllabus or your instructor. Collect two or three practice problems per topic from homework, textbook review exercises, or old exams if your instructor shares them.
Days 9 to 4. Do 30–40 minutes a day of mixed problems, without looking at your notes first. Mixing topics feels harder, and that's why it works (Six strategies for effective learning). Keep an error log: for each miss, write what went wrong and the fix.
Days 3 and 2. Take a timed practice exam. Spend the next day on your error log only, and bring the two hardest problems to the QRC.
The day before. Lightly review your error log and formulas, and read Common math errors. Sleep matters more than one more hour of problems.
Tip. To build a weekly study plan, meet with a coach at the Center for Academic Success.
Getting ready for the ALEKS placement
ALEKS decides where you start in Lawrence math: MATH 102, MATH 103, or calculus (MATH 140).
How it works. ALEKS adapts to your answers, so it measures what you know rather than how many questions you get right. Scores of 75 or more place into MATH 140, 45–74 into MATH 103, and below 45 into MATH 102 (ALEKS math placement).
Take it straight. Use only the tools the test gives you. A placement that's too high makes the course harder, not easier.
Check yourself first. The QRC self-check for MATH 102 or 103 shows which skills to review, with a worksheet for each.
If you want to place higher. After your first attempt, ALEKS gives you learning modules matched to your gaps. To retake the proctored test, wait 48 hours and spend at least five hours in the modules. Khan Academy and Paul's Online Notes: Algebra are good companions.
Not sure which course is right?. Talk with your adviser, or stop by the QRC during drop-in hours.
How to learn from a free textbook
Reading math isn't like reading a novel. Read with a pencil, and expect to go slowly.
The routine
- Skim the section headings and the boxed definitions first, so you know where you're going.
- For each worked example, cover the solution and try it yourself before reading it.
- Do the short practice problems right after each example. In OpenStax books these are labeled "Try It," and answers are in the back.
- If your course uses a different book, match by topic, not chapter number. Use the book's search or index.
Tip. Many Lawrence math courses use OpenStax books, so your course text may already be free (OpenStax textbook library). For extra practice with full solutions, the CLP Calculus texts and problem books problem books are hard to beat.
Getting the most out of math videos
Watching someone else solve a problem feels like learning. It only counts once you can do one yourself.
The routine
- Watch with paper and pencil, not in bed.
- Pause before each step and predict what comes next.
- Speed up the parts you know and slow down the parts you don't.
- Right after, do one problem on your own with the video closed.
- If three videos haven't helped, switch to a person. Come to the QRC.
Tip. Good places to start: Khan Academy for short skill videos, Professor Leonard lectures for full lectures, Essence of Calculus (3Blue1Brown) for the big ideas, and StatQuest for statistics.
Asking your professor for help
Office hours are for every student, not only for students in trouble. Professors like specific questions.
In person. Go to office hours with one or two specific problems and the work you've tried. It's fine to say, "I don't know where to start."
By email. Put the course and topic in the subject line. Say what you tried, ask one clear question, and attach a photo of your work.
Subject: MATH 140, question on 3.4 #12 Hi Professor ___, I'm working on problem 12 in section 3.4. I used the chain rule (my work is attached), but my answer doesn't match the back of the book. Is my setup right, or could I come to office hours Tuesday to go over it? Thanks, [Your name]
Your first shift as a QRC tutor
You don't need to know everything. You need a routine and the confidence to say, "Let's find out together."
Open (three minutes). Ask, "What's your goal today?" and "Show me where it stalled." Agree on at most two things to get done.
Work. Ask for decisions ("What tells you to use substitution here?"). Model one step, do the next together, then let them do one alone. When several students are waiting, give each a next step and rotate.
Close (three minutes). Have the student summarize what they learned in a sentence or two, and suggest when to practice again. Then write the session summary in Navigate.
When you don't know. Say so, and look it up together in Paul's Online Math Notes or the course text. Students learn a lot from watching how you get unstuck.
Tip. The QRC trains to the CRLA tutor training certification (ITTPC) standards. The scenarios in QMaSC Handbook: training and mentoring chapters make good practice.
Sending your students to the QRC
Students come when an instructor they trust names a specific reason to go.
Three things that help most
- Put a line about the QRC in your syllabus and on Canvas (sample below).
- Send the QRC your exam dates so we can plan review sessions and staffing.
- Mention the QRC the week before an exam, and name what tutors can help with.
Link to a topic. Each topic on this page has its own address. Add #calculus, #precalc, #stats, or #foundations to the end of this page's address to send students straight to that topic.
Free help: The Quantitative Resource Center (QRC) offers drop-in tutoring Sunday–Thursday, 6–9 p.m., on the second floor of Mudd Library. No appointment needed. The QRC Resource Directory lists free textbooks, videos, and practice for this course.
Tip. For building quantitative reasoning into your own course, start with Developing quantitative reasoning. For free textbooks, see AIM approved open textbooks.
Which statistics, data science, or CS course comes first?
A map of the course sequences in statistics, data science, and computer science, from the 2026–27 catalog. Check the official course descriptions before you register.
Statistics
- Start with STAT 107 (no prerequisite). If you have credit for MATH 140, BIOL 170, or AP Statistics, start with STAT 255 instead.
- STAT 255, Statistical Modeling, leads to STAT 455, Advanced Statistical Modeling.
- The theory path: MATH 155, then MATH 200 and MATH 230, then MATH/STAT 340 (Probability), then STAT 445 (Mathematical Statistics) or STAT 450 (Bayesian Statistics).
- Resources for each course: statistics.
Data science
- Start with DASC 110, Data Science I (or ANTH 207 or BIOL 280). Then DASC 210, Data Science II.
- DASC 420, Advanced Predictive Modeling, needs STAT 255 and MATH 205 or MATH 250.
- STAT/CMSC 208, Statistical Machine Learning, needs one of CMSC 140, CMSC 150, CMSC 205, or DASC 110.
- The major also needs MATH 140 and a linear algebra course: MATH 205 (Applied Linear Algebra, after MATH 140) or MATH 250.
- Resources for each course: data science and applied linear algebra.
Computer science
- Majors start with CMSC 150 (Java). CMSC 140 (Python) is designed for non-majors and also opens CMSC 225 and STAT 208.
- CMSC 250 needs a C− or better in CMSC 150, plus an ALEKS score of 75 or a C− or better in MATH 103.
- CMSC 270 (Data Structures, in C++) needs a C− or better in CMSC 250. Most 400-level courses need CMSC 270.
- CMSC 510 and 515 also need MATH 230. The major needs MATH 140, 155, and 230.
- Resources for each course: computer science.
If the math is the problem. CMSC 250 and MATH 205 both lean on the ALEKS 75 level. The QRC self-check shows which skills to work on for MATH 102, 103, 140, and 155.
Tip. Course numbers and prerequisites change. The data science and statistics and computer science course descriptions are the official word.
Start here at Lawrence
I want a person to help me, or I need to take the math placement. Free campus services. These are the first stop when you want a person rather than a link.
- ★ QRC drop-in tutoring (Lawrence University)
Peer tutors for 100- and 200-level math and Q-requirement courses. No appointment needed. Bring your work and a specific question if you can.
Start: Mudd Library, second floor, Sunday–Thursday, 6–9 p.m. Check the tutor board for who is on tonight. - ★ ALEKS math placement (Lawrence University, Department of Mathematics)
Required before math or physics courses. Scores of 75+ place into calculus (MATH 140), 45–74 into MATH 103, and below 45 into MATH 102. After your first attempt you get personalized ALEKS learning modules.
Start: To retake the proctored test, wait 48 hours and complete at least 5 hours in the learning modules. - ★ [Used at Lawrence] QRC course self-check (Quantitative Resource Center)
About 16 questions for MATH 102, 103, 140, or 155. You get a list of the skills to work on, in order, with a QRC worksheet and free resources for each. It isn't a placement test, and nothing you enter is saved.
Start: Pick the course you're in or headed to. - Course tutors through Navigate (Lawrence University, Center for Academic Success)
One-on-one and small-group content tutoring for specific courses, plus writing, oral communication, and multilingual support. Request a tutor in MyLU Navigate or ask your instructor.
Start: Check your course's Canvas site or syllabus for an assigned tutor first. - Center for Academic Success (Lawrence University)
Success coaching on time, motivation, and study habits, academic skills workshops, and peer tutoring programs. A good next step when the problem is bigger than one course.
Start: Mudd Library, second floor, weekdays 8 a.m.–5 p.m. Book a coaching meeting from the CAS page. - Mathematics course descriptions (Lawrence University, Department of Mathematics)
Official descriptions and prerequisites for every math course, from MATH 102 (Foundations in Math) through calculus and beyond. MATH 103 and 140 need an ALEKS score (45 and 75) or a C− or better in the course before.
Start: The course catalog is the official source for planning. - [Used at Lawrence] Data science and statistics course descriptions (Data Science and Statistics, Lawrence University)
The department's official list of DASC and STAT courses, with prerequisites. Check it before you plan a sequence. - [Used at Lawrence] Computer science course descriptions (Computer Science, Lawrence University)
The department's official list of CMSC courses, with prerequisites and the languages each course uses. - Seeley G. Mudd Library (Lawrence University)
Research help, data and systems librarianship, course reserves, and quiet study space. The QRC and CAS are on the library's second floor.
Start: Ask at the main desk for help finding data or a statistics text. - [Used at Lawrence] OpenStax textbook library (OpenStax, Rice University)
Free, peer-reviewed textbooks in math, statistics, the sciences, economics, and more. Lawrence's intro math courses use OpenStax texts, so your assigned book may already be free here as a web page, PDF, or app.
Start: Check your syllabus for the book title, then find it by subject.
Foundations and catching up
I'm rusty on fractions, algebra, or the basics, or I'm preparing for ALEKS. Arithmetic through intermediate algebra. Matches MATH 102 and the early part of MATH 103.
Start here: basics and algebra
Stuck right now · 10 minutes. Name the skill (fractions, exponents, factoring) and search for it on Khan Academy. Watch one video, then do the practice set until you get three in a row.
Behind on a topic · an evening. Read the matching section of Prealgebra 2e or Intermediate Algebra 2e and work the "Try It" problems. Then read Common math errors. Most algebra trouble is on that page.
Rebuilding a skill · a few weeks. Use a Khan Academy unit test or course challenge to find your gaps, then spend 20 minutes a day on only those. Preparing for placement? See Getting ready for the ALEKS placement. Not sure which skills? Take the MATH 102 self-check.
Tip. Fractions and negative signs cause more trouble than anything else at this level. If they feel shaky, start there.
- ★ Khan Academy (Khan Academy (nonprofit))
Short videos and unlimited practice with instant feedback, arranged in mastery units. Good for filling a specific gap (negative numbers, fractions, factoring) without redoing a whole course.
Start: Use a unit test or course challenge to find your gaps, then work only those skills. - ★ [Used at Lawrence] Prealgebra 2e (OpenStax, Rice University)
A complete, peer-reviewed text on whole numbers, fractions, decimals, percents, and an introduction to algebra. Every section has worked examples followed by "try it" problems with answers.
Start: The fractions and decimals chapters are the most-used review. - ★ Paul's Online Math Notes (Paul Dawkins, Lamar University)
Clear class notes with many worked examples for algebra through differential equations, with practice problems and solutions. Students often find these easier to read than their textbook. It also has review pages on algebra and trig for calculus students.
Start: For a quick refresher, try the Algebra/Trig Review under Extras, or the cheat sheets. - [Used at Lawrence] QRC course self-check (Quantitative Resource Center)
About 16 questions for MATH 102, 103, 140, or 155. You get a list of the skills to work on, in order, with a QRC worksheet and free resources for each. It isn't a placement test, and nothing you enter is saved.
Start: Pick the course you're in or headed to. - [Used at Lawrence] Intermediate Algebra 2e (OpenStax, Rice University)
Linear equations, systems, polynomials, rational expressions, radicals, and quadratics, with lots of practice. A good bridge from MATH 102 into MATH 103.
Start: Use the chapter review exercises as a self-check before an exam. - Algebra, trig, and calculus cheat sheets (Paul Dawkins, Lamar University)
Printable reference sheets: algebra rules, common errors, trig identities, and derivative and integral tables. The "common algebra errors" sheet is useful before any exam.
Start: Print the algebra sheet for your notebook. - Common math errors (Paul Dawkins, Lamar University)
A short catalog of the algebra and calculus mistakes Paul Dawkins sees most often, each with the correct version. A good page to read the night before an exam. - Professor Leonard lectures (Leonard (community college instructor), YouTube)
Full-length, unhurried classroom lectures on intermediate algebra, precalculus, Calculus I–III, statistics, and differential equations. They're long, but students who want every step written out love them.
Start: Search the channel for your exact topic rather than starting at lecture 1.
Functions, precalculus, and trigonometry
I'm in MATH 103 or getting ready for calculus. Functions, graphs, exponentials and logarithms, and trigonometry.
Start here: precalculus
Stuck right now · 10 minutes. Graph it. Type the function into Desmos graphing calculator and add a slider for the number you're unsure about. Watch what changes.
Behind on a topic · an evening. Read the matching section of Precalculus 2e, then work examples from Paul's Online Notes: Algebra, which has full solutions.
Rebuilding a skill · a few weeks. Functions, exponentials and logarithms, and trigonometry are the backbone of calculus. Work through Paul's Online Notes: Algebra/Trig Review one topic a day. Not sure which skills? Take the MATH 103 self-check.
Tip. Logarithms trip up many MATH 103 students. A logarithm undoes an exponential: log_b(x) = y means b^y = x. Every log rule comes from an exponent rule.
- ★ [Used at Lawrence] Precalculus 2e (OpenStax, Rice University)
Functions, polynomial and rational functions, exponentials and logarithms, trigonometry, and conics. Clean examples and many practice problems with odd answers in the back.
Start: Chapter 1 (functions) and chapter 4 (exponential and logarithmic functions) match the core of MATH 103. - ★ Paul's Online Notes: Algebra (Paul Dawkins, Lamar University)
Clear notes with many worked examples on equations, functions, polynomial and rational functions, exponentials and logarithms, and systems. Each section has practice problems with full solutions.
Start: The Exponential and Logarithm Functions chapter is a common MATH 103 rescue. - ★ Professor Leonard lectures (Leonard (community college instructor), YouTube)
Full-length, unhurried classroom lectures on intermediate algebra, precalculus, Calculus I–III, statistics, and differential equations. They're long, but students who want every step written out love them.
Start: Search the channel for your exact topic rather than starting at lecture 1. - [Used at Lawrence] QRC course self-check (Quantitative Resource Center)
About 16 questions for MATH 102, 103, 140, or 155. You get a list of the skills to work on, in order, with a QRC worksheet and free resources for each. It isn't a placement test, and nothing you enter is saved.
Start: Pick the course you're in or headed to. - Algebra, trig, and calculus cheat sheets (Paul Dawkins, Lamar University)
Printable reference sheets: algebra rules, common errors, trig identities, and derivative and integral tables. The "common algebra errors" sheet is useful before any exam.
Start: Print the algebra sheet for your notebook. - Common math errors (Paul Dawkins, Lamar University)
A short catalog of the algebra and calculus mistakes Paul Dawkins sees most often, each with the correct version. A good page to read the night before an exam. - [Used at Lawrence] College Algebra 2e (OpenStax, Rice University)
The algebra half of precalculus without trigonometry: equations, inequalities, functions, and systems.
Start: Use it when your course is algebra-heavy and you want more practice than your text offers. - Precalculus (Stitz and Zeager) (Carl Stitz and Jeff Zeager)
A widely adopted open precalculus text with careful explanations, available as PDF and as interactive online lessons. Approved by the American Institute of Mathematics.
Start: Its function chapters explain why, not just how. - Paul's Online Notes: Algebra/Trig Review (Paul Dawkins, Lamar University)
A self-test of the algebra and trig that calculus assumes: exponents, logarithms, trig functions and identities, and solving equations. Each problem has a worked solution.
Start: Do one topic a day alongside your calculus course.
Geometry and further trigonometry
I want more trig or geometry than precalculus had time for. Laws of sines and cosines, polar coordinates, conics, proofs in plane geometry, and the trig that calculus and physics lean on.
Start here: geometry and further trig
Stuck right now · 10 minutes. Draw it. Label every known side and angle, then decide whether you have a right triangle or need the laws of sines and cosines.
Behind on a topic · an evening. Read the chapter on further applications of trigonometry in Precalculus 2e (laws of sines and cosines, polar coordinates, vectors) or the general-triangles chapter of Trigonometry (Corral).
Rebuilding a skill · a few weeks. For geometry with proofs, work through Book I of Euclid's Elements (David Joyce's edition), constructing each figure in GeoGebra as you go.
Tip. Calculus and physics use the unit circle, the Pythagorean identity, and similar triangles constantly. Time spent here pays off later.
- ★ Trigonometry (Corral) (Michael Corral, Schoolcraft College)
A free, careful trigonometry text that goes well past a precalculus course: general triangles and the laws of sines and cosines, identities, radian measure, graphing, inverse functions, and complex numbers.
Start: The chapter on general triangles: laws of sines and cosines. - ★ Euclid's Elements (David Joyce's edition) (David E. Joyce, Clark University)
The full Elements online, with a diagram and a short modern commentary for every proposition. The classic place to learn plane geometry and proof together.
Start: Book I, propositions 1–48, ending with the Pythagorean theorem. - [Used at Lawrence] Precalculus 2e (OpenStax, Rice University)
Functions, polynomial and rational functions, exponentials and logarithms, trigonometry, and conics. Clean examples and many practice problems with odd answers in the back.
Start: Chapter 1 (functions) and chapter 4 (exponential and logarithmic functions) match the core of MATH 103. - GeoGebra (GeoGebra)
Graphing, geometry, 3D, and computer algebra in one free tool, with thousands of ready-made activities.
Calculus
I'm in MATH 140 or a calculus course like it. Free textbooks with worked examples, lecture series, and problem books with answers.
Start here: calculus
Stuck right now · 10 minutes. Find your topic in Paul's Online Notes: Calculus I, II, and III and read the worked example closest to your problem.
Behind on a topic · an evening. Read the section in Calculus, Volumes 1–3, then do problems from the CLP Calculus texts and problem books problem books, which give hints, answers, and full solutions.
Rebuilding a skill · a few weeks. Weak algebra is the most common reason calculus feels hard. Spend 15 minutes a day on Paul's Online Notes: Algebra/Trig Review alongside your course. For the big ideas, watch Essence of Calculus (3Blue1Brown). Not sure which skills? Take the MATH 140 or 155 self-check.
Tip. Most calculus mistakes are algebra mistakes. Check Common math errors before you decide you don't understand the calculus.
- ★ CLP Calculus texts and problem books (Feldman, Rechnitzer, and Yeager, University of British Columbia)
Four free texts (differential, integral, multivariable, and vector calculus), each with a separate problem book that has hints, answers, and full solutions. The problem books are the best free source of calculus practice we know.
Start: CLP-1 problem book for derivatives; CLP-2 for integrals. - ★ [Used at Lawrence] Calculus, Volumes 1–3 (OpenStax, Rice University)
A conventional three-volume calculus sequence, similar in layout to commercial textbooks. Useful as a second explanation of any standard topic.
Start: Volume 1 covers limits, derivatives, and an introduction to integration. - ★ Paul's Online Notes: Calculus I, II, and III (Paul Dawkins, Lamar University)
Many students find these easier to read than their textbook: short explanations, lots of worked examples, and practice problems with step-by-step solutions for limits, derivatives, integrals, series, and multivariable calculus.
Start: Calculus I for MATH 140. Calculus II and III are linked from the site's menu. - [Used at Lawrence] QRC course self-check (Quantitative Resource Center)
About 16 questions for MATH 102, 103, 140, or 155. You get a list of the skills to work on, in order, with a QRC worksheet and free resources for each. It isn't a placement test, and nothing you enter is saved.
Start: Pick the course you're in or headed to. - Algebra, trig, and calculus cheat sheets (Paul Dawkins, Lamar University)
Printable reference sheets: algebra rules, common errors, trig identities, and derivative and integral tables. The "common algebra errors" sheet is useful before any exam.
Start: Print the algebra sheet for your notebook. - Common math errors (Paul Dawkins, Lamar University)
A short catalog of the algebra and calculus mistakes Paul Dawkins sees most often, each with the correct version. A good page to read the night before an exam. - Paul's Online Notes: Algebra/Trig Review (Paul Dawkins, Lamar University)
A self-test of the algebra and trig that calculus assumes: exponents, logarithms, trig functions and identities, and solving equations. Each problem has a worked solution.
Start: Do one topic a day alongside your calculus course. - Active Calculus (Matt Boelkins and collaborators)
Built around short activities that ask you to work out ideas before they are stated. Good for understanding why derivatives and integrals work, not just the rules.
Start: Try the "preview activity" at the start of a section before reading it. - APEX Calculus (Gregory Hartman and collaborators)
A complete open calculus text with interactive 3D graphics in the online version. Approved by the American Institute of Mathematics. - MIT 18.01SC Single Variable Calculus (MIT OpenCourseWare)
A full self-study calculus course: lecture videos, short recitation videos by teaching assistants, problem sets, and exams with solutions.
Start: The recitation videos walk through one problem each and are good for a single stuck topic. - Essence of Calculus (3Blue1Brown) (Grant Sanderson)
A short animated series on the big ideas of calculus: derivatives as rates, integrals as accumulation, and why the two are connected. Best watched before or alongside a course, not instead of practice. - Professor Leonard lectures (Leonard (community college instructor), YouTube)
Full-length, unhurried classroom lectures on intermediate algebra, precalculus, Calculus I–III, statistics, and differential equations. They're long, but students who want every step written out love them.
Start: Search the channel for your exact topic rather than starting at lecture 1.
Multivariable and vector calculus
I'm in MATH 155, or I want to go past it to Green's, Stokes', and the divergence theorems. Vectors, partial derivatives, multiple integrals, and vector calculus: line integrals, path independence, and the big theorems.
Start here: multivariable calculus
Stuck right now · 10 minutes. Find your topic in Paul's Online Notes: Calculus III and read the worked example closest to your problem.
Behind on a topic · an evening. Read the matching section of Calculus, Volume 3 and watch the Khan Academy: Multivariable calculus video on the same idea. The pictures matter more here than in single-variable calculus.
Going past MATH 155 · a few weeks. Path independence, Green's theorem, curl and divergence, Stokes' theorem, and the divergence theorem are all in Chapter 6 of Calculus, Volume 3 and the last chapters of Paul's Online Notes: Calculus III. MIT 18.02SC Multivariable Calculus has problem sets with solutions for all of them.
Tip. Most of vector calculus is one idea: integrating a derivative over a region equals integrating the original function over the boundary. The Fundamental Theorem, Green's, Stokes', and the divergence theorem are all versions of it.
- ★ Calculus, Volume 3 (OpenStax, Rice University)
Free multivariable text: vectors, curves, partial derivatives, and multiple integrals, then a full vector calculus chapter with line integrals, conservative fields and path independence, Green's theorem, surface integrals, Stokes' theorem, and the divergence theorem.
Start: Chapter 6, Vector Calculus, for everything past MATH 155. - ★ Paul's Online Notes: Calculus III (Paul Dawkins, Lamar University)
Worked-example notes for all of multivariable calculus, through line integrals, the fundamental theorem for line integrals (path independence), Green's theorem, curl and divergence, surface integrals, Stokes' theorem, and the divergence theorem.
Start: The Line Integrals and Surface Integrals chapters go past MATH 155. - ★ Khan Academy: Multivariable calculus (Khan Academy (videos by Grant Sanderson of 3Blue1Brown))
Visual video lessons on partial derivatives, gradients, multiple integrals, and the vector calculus theorems, with especially clear treatments of divergence, curl, Green's, Stokes', and the divergence theorem. - CLP Calculus texts and problem books (Feldman, Rechnitzer, and Yeager, University of British Columbia)
Four free texts (differential, integral, multivariable, and vector calculus), each with a separate problem book that has hints, answers, and full solutions. The problem books are the best free source of calculus practice we know.
Start: CLP-1 problem book for derivatives; CLP-2 for integrals. - Paul's Online Notes: Calculus I, II, and III (Paul Dawkins, Lamar University)
Many students find these easier to read than their textbook: short explanations, lots of worked examples, and practice problems with step-by-step solutions for limits, derivatives, integrals, series, and multivariable calculus.
Start: Calculus I for MATH 140. Calculus II and III are linked from the site's menu. - MIT 18.02SC Multivariable Calculus (MIT OpenCourseWare)
A full self-study course with lecture videos, recitation videos, problem sets, and exams with solutions, including matrices, Green's theorem, Stokes' theorem, and the divergence theorem.
Applied linear algebra
I'm in MATH 205, or I want the matrix math behind regression, PCA, and machine learning. Vectors, matrices, least squares, eigenvectors, and gradient descent, taught through data: regression, principal components, and networks.
Start here: applied linear algebra
Stuck right now · 10 minutes. Watch the matching chapter of Essence of Linear Algebra (3Blue1Brown). Each one is about 10 minutes and shows what a matrix does to space, which makes most of the rules make sense.
Behind on a topic · an evening. Read the matching section of Introduction to Applied Linear Algebra (VMLS), which teaches vectors, matrices, and least squares through data. For pictures you can drag, use Interactive Linear Algebra.
Rebuilding a skill · a few weeks. Build something: fit a line to real data by least squares in Google Colab or R, then by gradient descent, and compare. Introduction to Applied Linear Algebra (VMLS) walks through the first; the Neural networks (3Blue1Brown) videos explain the second. When you want more, MIT 18.065: Matrix Methods in Data Analysis, Signal Processing, and Machine Learning covers the SVD and PCA.
Tip. Three ideas carry most of MATH 205: a matrix is a way to handle many numbers at once, least squares is the best answer to a system with no exact answer, and the gradient points the way downhill.
- ★ Essence of Linear Algebra (3Blue1Brown) (Grant Sanderson)
Animated videos that show matrices as transformations of space. Many students say this is when linear algebra finally made sense. - ★ Introduction to Applied Linear Algebra (VMLS) (Stephen Boyd and Lieven Vandenberghe)
Vectors, matrices, and least squares, taught through applications to data: clustering, regression, and model fitting. A gentle way into matrix algebra with very little proof. Approved by the American Institute of Mathematics.
Start: Chapters 6–10 for matrix algebra. - ★ Interactive Linear Algebra (Dan Margalit and Joseph Rabinoff, Georgia Tech)
A free linear algebra text with interactive pictures you can drag: systems, matrix transformations, determinants, eigenvectors, and orthogonality, including least squares.
Start: Chapter 3 for matrices as transformations. - StatQuest (Josh Starmer, YouTube)
Short, friendly videos that explain statistical and machine-learning ideas (p-values, regression, PCA) one picture at a time. - Mathematics for Machine Learning (Deisenroth, Faisal, and Ong (Cambridge University Press))
The linear algebra, vector calculus, probability, and optimization behind machine learning, applied to regression, PCA, and classification. Approved by the American Institute of Mathematics.
Start: Chapter 5, Vector Calculus, and Chapter 7, Continuous Optimization. - Neural networks (3Blue1Brown) (Grant Sanderson)
An animated series on how neural networks learn. Gradient descent is calculus as optimization, and backpropagation is the chain rule at scale.
Start: The videos on gradient descent and backpropagation calculus. - MIT 18.065: Matrix Methods in Data Analysis, Signal Processing, and Machine Learning (Gilbert Strang, MIT OpenCourseWare)
Strang's lectures on the linear algebra of data: the SVD, PCA, least squares, and gradient descent. Best after a first pass through MATH 205, or alongside MATH 355.
Linear algebra and differential equations
I'm in MATH 250 or 350, or I need linear algebra or differential equations for physics, chemistry, or economics. Free, well-regarded texts and video series for proof-based linear algebra and ordinary differential equations.
Start here: linear algebra and differential equations
Stuck right now · 10 minutes. Watch the Essence of Linear Algebra (3Blue1Brown) video on your topic to see the geometry.
Behind on a topic · an evening. Read the section in Understanding Linear Algebra and do its activities. For differential equations, use Paul's Online Notes: Differential Equations.
Rebuilding a skill · a few weeks. MIT 18.06SC Linear Algebra is a full course with problem sets and solutions.
Tip. Many linear algebra questions get easier when you ask what the matrix does to a vector.
- ★ Understanding Linear Algebra (David Austin, Grand Valley State University)
An open text that emphasizes geometric meaning and applications, with interactive computation built into the online version. - ★ Essence of Linear Algebra (3Blue1Brown) (Grant Sanderson)
Animated videos that show matrices as transformations of space. Many students say this is when linear algebra finally made sense. - ★ Introduction to Applied Linear Algebra (VMLS) (Stephen Boyd and Lieven Vandenberghe)
Vectors, matrices, and least squares, taught through applications to data: clustering, regression, and model fitting. A gentle way into matrix algebra with very little proof. Approved by the American Institute of Mathematics.
Start: Chapters 6–10 for matrix algebra. - Professor Leonard lectures (Leonard (community college instructor), YouTube)
Full-length, unhurried classroom lectures on intermediate algebra, precalculus, Calculus I–III, statistics, and differential equations. They're long, but students who want every step written out love them.
Start: Search the channel for your exact topic rather than starting at lecture 1. - MIT 18.06SC Linear Algebra (Gilbert Strang, MIT OpenCourseWare)
Strang's well-known lectures with recitation videos, problem sets, and exams with solutions. - Notes on Diffy Qs (Jiří Lebl)
A free introductory differential equations text covering first-order equations, linear systems, Fourier series, and Laplace transforms. Approved by the American Institute of Mathematics. - Paul's Online Notes: Differential Equations (Paul Dawkins, Lamar University)
Worked-example notes on first-order equations, second-order linear equations, Laplace transforms, systems, and series solutions, with practice problems. - Interactive Linear Algebra (Dan Margalit and Joseph Rabinoff, Georgia Tech)
A free linear algebra text with interactive pictures you can drag: systems, matrix transformations, determinants, eigenvectors, and orthogonality, including least squares.
Start: Chapter 3 for matrices as transformations.
Proof, logic, and discrete math
I'm in MATH 230, learning to write proofs, or working with formal logic. Symbolic reasoning: proofs, sets, logic, counting, and graphs.
Start here: discrete math and proofs
Stuck right now · 10 minutes. Write out the definition of every term in the statement. Most proofs begin by unpacking definitions.
Behind on a topic · an evening. Read the matching section of Discrete Structures, then the chapter of Book of Proof on the method you're using: direct proof, contrapositive, contradiction, or induction.
Rebuilding a skill · a few weeks. Work a few exercises from each proof-technique chapter of Book of Proof. Bring drafts to the QRC. Proof writing gets better with a reader.
Tip. Before you try to prove something, test it on small examples. They often show you why it's true.
- ★ [Used at Lawrence] Discrete Structures (Kyle Ormsby and David Perkinson, Reed College)
The text for MATH 230, Discrete Mathematics, which comes after MATH 155. Written for Reed's Math 113, it covers counting, sets, graph theory, probability, number theory and modular arithmetic, and generating functions.
Start: Reed's Math 113 course page (people.reed.edu/~davidp/113/) has lecture videos and review sheets that follow the book. - ★ Book of Proof (Richard Hammack)
A gentle, popular introduction to sets, logic, and proof techniques (direct, contrapositive, contradiction, induction). Many exercises have solutions.
Start: Part II, on how to write a proof, is the core. - forall x: Calgary (P. D. Magnus, Tim Button, and the Open Logic Project)
An open introduction to formal logic: truth tables, natural deduction, and first-order logic. Used in many philosophy and logic courses. - Discrete Mathematics: An Open Introduction (Oscar Levin)
Counting, sequences, logic and proofs, and graph theory, written for students meeting proofs for the first time. Approved by the American Institute of Mathematics.
Statistics and probability
I'm in STAT 107, 255, or 340, or I'm using statistics in psychology, biology, or economics. Lawrence's statistics sequence runs from STAT 107 or STAT 255 through probability (MATH/STAT 340) to mathematical, Bayesian, and advanced modeling courses.
Start here: statistics
Stuck right now? Find the idea in Seeing Theory and play with the picture until the definition makes sense. Then find your course below.
STAT 107 · Principles of Statistics. OpenIntro Statistics covers the whole course, with guided practice that has answers. The apps in Art of Stat web apps simulate what confidence intervals and p-values mean. Have credit for MATH 140, BIOL 170, or AP Statistics? Take STAT 255 instead.
STAT 255 · Statistical Modeling. Start with STAT 255 course notes, Lawrence's own notes. For more practice with permutation tests and the bootstrap, use StatKey and Introduction to Modern Statistics. Statistical Inference via Data Science (ModernDive) does regression and resampling in R, and StatQuest has a short video on nearly every model.
MATH/STAT 340 · Probability. Statistics 110: Probability (Harvard) has lectures, practice problems with solutions, and a free textbook. Introduction to Probability (Grinstead and Snell) has more worked examples. The course needs MATH 200 and 230: brush up on series in Paul's Online Notes: Calculus I, II, and III and counting in Discrete Structures.
400 level · STAT 445, 450, 455. Bayes Rules! for Bayesian statistics (STAT 450) and Beyond Multiple Linear Regression for generalized linear and multilevel models (STAT 455). For STAT 445, the resampling chapters of STAT 255 course notes and Introduction to Modern Statistics build the intuition for permutation tests and bootstrap intervals that the course makes rigorous.
Tip. Not sure which course comes next? See the course-sequence guide, or check the official course descriptions.
- ★ OpenIntro Statistics (Diez, Çetinkaya-Rundel, and Barr)
One of the most widely used free intro statistics texts, with real data sets, video overviews, and labs in R. Approved by the American Institute of Mathematics. - ★ Seeing Theory (Daniel Kunin, Brown University)
A visual introduction to probability and statistics in six interactive chapters, from basic probability through regression. Lets you watch the central limit theorem happen.
Start: Chapter 3, Probability Distributions. - ★ [Used at Lawrence] STAT 255 course notes (Andrew Sage, Lawrence University)
Lawrence's own notes for STAT 255 (posted when it was called Statistics for Data Science), in R: exploring data, permutation tests, bootstrap intervals, regression, building models, prediction, and logistic regression. The posted version is from 2023, so check it against your syllabus.
Start: Chapters 3 and 4 for permutation tests and the bootstrap. - [Used at Lawrence] Data science and statistics course descriptions (Data Science and Statistics, Lawrence University)
The department's official list of DASC and STAT courses, with prerequisites. Check it before you plan a sequence. - Professor Leonard lectures (Leonard (community college instructor), YouTube)
Full-length, unhurried classroom lectures on intermediate algebra, precalculus, Calculus I–III, statistics, and differential equations. They're long, but students who want every step written out love them.
Start: Search the channel for your exact topic rather than starting at lecture 1. - Introduction to Modern Statistics (Mine Çetinkaya-Rundel and Johanna Hardin (OpenIntro))
A modern intro text that teaches inference through randomization and bootstrapping before formulas, with an emphasis on data and modeling. - Introductory Statistics 2e (OpenStax, Rice University)
A traditional one-term statistics text: descriptive statistics, probability, distributions, confidence intervals, and hypothesis tests. - Art of Stat web apps (Bernhard Klingenberg)
Free browser apps for exploring data, regression, distributions, sampling distributions, and inference, including bootstrap and permutation tests. Useful when you don't have statistical software. - StatQuest (Josh Starmer, YouTube)
Short, friendly videos that explain statistical and machine-learning ideas (p-values, regression, PCA) one picture at a time. - jamovi (The jamovi project)
Point-and-click statistics software, a free alternative to SPSS, built on R. Good for students who need t-tests, ANOVA, or regression without writing code. - StatKey (Lock, Lock, Lock Morgan, Lock, and Lock)
Free in-browser apps for bootstrap intervals, randomization tests, and sampling distributions. Click to resample and watch the distribution build up.
Start: Try "Bootstrap Confidence Interval" with one of the built-in data sets. - Statistics 110: Probability (Harvard) (Joe Blitzstein, Harvard University)
A full probability course: lecture videos, handouts, practice problems with solutions, and a free PDF of Blitzstein and Hwang's textbook. Covers nearly everything in MATH/STAT 340, with the same emphasis on counting, conditioning, and named distributions.
Start: The strategic practice problems, which come with full solutions. - Introduction to Probability (Grinstead and Snell) (Charles Grinstead and J. Laurie Snell)
A classic free probability text with many worked examples and a computational flavor: simulation, generating functions, Markov chains, and the limit theorems. Approved by the American Institute of Mathematics. - Bayes Rules! (Alicia Johnson, Miles Ott, and Mine Dogucu)
A friendly introduction to Bayesian modeling in R: priors and posteriors, simulation, MCMC, regression, and hierarchical models. Matches the topics of STAT 450. - Beyond Multiple Linear Regression (Paul Roback and Julie Legler)
Generalized linear models and multilevel (mixed-effects) models in R, built around real case studies. The natural next step after STAT 255, and close to the STAT 455 topic list. - Statistical Inference via Data Science (ModernDive) (Chester Ismay and Albert Y. Kim)
Data wrangling and visualization in R, then regression and inference by resampling (bootstrap and permutation tests). A good bridge from DASC 110 to STAT 255. - An Introduction to Statistical Learning (James, Witten, Hastie, and Tibshirani)
The standard free text for machine learning with a statistical view: regression, classification, resampling, trees, support vector machines, and unsupervised learning. Comes in R and Python editions, with labs and free video lectures.
Start: Chapter 2 for the big ideas: prediction versus inference, and the bias-variance trade-off.
Data science
I'm in DASC 110, 210, or 420, STAT 208, or CMSC/STAT 205, or I'm working toward the data science major or minor. Data work in R from Data Science I through predictive modeling: importing, wrangling, visualizing, modeling, and sharing results.
Start here: data science
Stuck on code right now? Copy the exact error message into a search, then check the matching chapter of R for Data Science (2e). Most errors in a first course are a missing package, a typo in a column name, or a missing comma. Then find your course below.
DASC 110 · Data Science I. Work through R for Data Science (2e) alongside the course, in Posit Cloud if you don't want to install anything. Data Science in a Box has slides and exercises on the same topics, including data ethics.
DASC 210 · Data Science II. Functions and iteration are in R for Data Science (2e). For the newer pieces: Text Mining with R for text data, Mastering Shiny for interactive apps, and Happy Git and GitHub for the useR for Git and GitHub.
STAT 255 · Statistical Modeling. See the statistics page. Start with STAT 255 course notes and Statistical Inference via Data Science (ModernDive).
STAT 208 and DASC 420 · Machine learning and predictive modeling. An Introduction to Statistical Learning is the standard text, with R and Python labs. Tidy Modeling with R shows how to fit and compare models in R. DASC 420 also needs MATH 205 or 250: see applied linear algebra.
CMSC/STAT 205 and 405 · Data-scientific programming. Start with R for Data Science (2e). For STAT 405, Advanced R and R Packages explains how R works underneath and how to write your own package.
Tip. Keep your raw data in its own file that you never edit, and put every cleaning step in code. Then you can always rerun your analysis from the start.
- ★ R for Data Science (2e) (Wickham, Çetinkaya-Rundel, and Grolemund)
The standard free introduction to doing data analysis in R with the tidyverse: importing, cleaning, visualizing, and summarizing data.
Start: The "Whole game" chapters get you to a working analysis fast. - ★ Data Science in a Box (Mine Çetinkaya-Rundel)
Slides, videos, and exercises from a first course in data science with R and the tidyverse: visualization, wrangling, data ethics, and communication. Close to the DASC 110 topic list.
Start: "Hello world" and "Exploring data" units. - ★ An Introduction to Statistical Learning (James, Witten, Hastie, and Tibshirani)
The standard free text for machine learning with a statistical view: regression, classification, resampling, trees, support vector machines, and unsupervised learning. Comes in R and Python editions, with labs and free video lectures.
Start: Chapter 2 for the big ideas: prediction versus inference, and the bias-variance trade-off. - [Used at Lawrence] Data science and statistics course descriptions (Data Science and Statistics, Lawrence University)
The department's official list of DASC and STAT courses, with prerequisites. Check it before you plan a sequence. - StatQuest (Josh Starmer, YouTube)
Short, friendly videos that explain statistical and machine-learning ideas (p-values, regression, PCA) one picture at a time. - [Used at Lawrence] STAT 255 course notes (Andrew Sage, Lawrence University)
Lawrence's own notes for STAT 255 (posted when it was called Statistics for Data Science), in R: exploring data, permutation tests, bootstrap intervals, regression, building models, prediction, and logistic regression. The posted version is from 2023, so check it against your syllabus.
Start: Chapters 3 and 4 for permutation tests and the bootstrap. - Posit Cloud (Posit)
RStudio in a web browser, so you can run R without installing anything. - Statistical Inference via Data Science (ModernDive) (Chester Ismay and Albert Y. Kim)
Data wrangling and visualization in R, then regression and inference by resampling (bootstrap and permutation tests). A good bridge from DASC 110 to STAT 255. - Happy Git and GitHub for the useR (Jenny Bryan)
How to set up Git and GitHub with R and RStudio, step by step, and how to use version control on a real project. The standard reference when Git won't cooperate.
Start: The installation chapters, in order, then "Connect RStudio to Git and GitHub." - Mastering Shiny (Hadley Wickham)
How to build interactive web apps from R with Shiny, from a first app to reactive programming. For the interactive visualization part of DASC 210.
Start: Chapters 1–3 get a working app on screen. - Text Mining with R (Julia Silge and David Robinson)
Working with text as data using tidy tools: word counts, sentiment, tf-idf, and topic models. Useful for the text-data unit of DASC 210 and for projects in the humanities and social sciences. - Tidy Modeling with R (Max Kuhn and Julia Silge)
How to fit, tune, and compare predictive models in R with the tidymodels packages: data splitting, resampling, preprocessing recipes, and model evaluation. - Advanced R and R Packages (Hadley Wickham (R Packages with Jennifer Bryan))
How R works under the hood: functions, environments, functional programming, and performance. Its companion, R Packages (r-pkgs.org), covers writing your own package. Both match STAT/CMSC 405. - The Missing Semester of Your CS Education (MIT)
Short lectures on the tools courses assume you know: the command line, text editors, Git, debugging, and scripting.
Computer science and programming
I'm in an intro CMSC course, learning Python, Java, or C++, or heading into data structures. Free books, visualizers, and practice for the intro sequence: Python (CMSC 140 and 210), Java (CMSC 150 and 250), and C++ (CMSC 270), plus the web (CMSC 106) and databases (CMSC 225).
Start here: computer science
Stuck right now? Cut your program down to the smallest piece that misbehaves, paste it into Python Tutor (it handles Python, Java, and C++), and step through it line by line. Then find your course below.
CMSC 140 and 210 · Python. Think Python (3rd ed.) is short and clear, and runs in Google Colab. Python for Everybody has videos for every chapter. CMSC 210 adds numerical work: see applied linear algebra for the matrix side.
CMSC 150 · Introduction to Computer Science (Java). Read the early chapters of Introduction to Programming Using Java. CS50x: Introduction to Computer Science is a good second explanation of loops, functions, and arrays, even though it isn't in Java.
CMSC 250 · Intermediate Programming (Java). The later chapters of Introduction to Programming Using Java cover GUIs, exceptions, threads, networking, and files, in about the order the course does.
CMSC 270 · Data Structures (C++). LearnCpp.com for the C++ itself, Open Data Structures for the data structures, and VisuAlgo to watch trees, heaps, and graph algorithms work.
CMSC 106 and 225 · The web and databases. MDN: Learn web development for HTML, CSS, and JavaScript. SQLBolt for SQL.
Beyond · CMSC 510 and 515. Both need MATH 230: see discrete math and proofs. Open Data Structures and VisuAlgo still help with algorithm analysis.
Tip. Read the first line of an error message slowly. It usually names the file, the line, and what went wrong. The Missing Semester of Your CS Education teaches the command line and Git that courses often assume.
- ★ Python Tutor (Philip Guo)
Paste in a short program and step through it line by line, with pictures of every variable, list, object, and pointer. Works for Python, Java, C++, C, and JavaScript, so it covers the whole intro sequence.
Start: Paste the smallest piece of code that misbehaves and click "Visualize Execution." - ★ Think Python (3rd ed.) (Allen Downey)
A short, clear introduction to programming in Python that teaches how to think about programs, not just syntax. Each chapter is a notebook you can run in Google Colab. - ★ Introduction to Programming Using Java (David Eck, Hobart and William Smith Colleges)
A complete free Java textbook. The early chapters cover CMSC 150 (programming basics, objects, and classes); the later ones cover CMSC 250 (GUIs, exceptions, threads, networking, and files).
Start: Chapter 2 for basics, Chapter 5 for objects and classes. - [Used at Lawrence] Computer science course descriptions (Computer Science, Lawrence University)
The department's official list of CMSC courses, with prerequisites and the languages each course uses. - Python for Everybody (Charles Severance, University of Michigan)
A complete beginner's course in Python with a free textbook, video lectures, and auto-graded exercises. Assumes no programming background. - Google Colab (Google)
Python notebooks that run in the browser with common data libraries already installed. - LearnCpp.com (Alex and contributors)
A thorough, free C++ tutorial that starts from scratch. Useful when CMSC 270 moves from Java to C++: pointers, references, memory, and classes. - Open Data Structures (Pat Morin)
A free data structures text with editions in C++, Java, and pseudocode: lists, hash tables, trees, heaps, and graphs, with running-time analysis. - VisuAlgo (Steven Halim, National University of Singapore)
Animations of sorting, linked lists, trees, heaps, hash tables, and graph algorithms. Step through an algorithm on your own input to see why it works. - CS50x: Introduction to Computer Science (David Malan, Harvard University)
Harvard's free intro course: lectures, short videos, and problem sets in C, Python, SQL, and web programming. A good second explanation of almost any intro topic. - MDN: Learn web development (Mozilla)
The standard free reference and course for HTML, CSS, and JavaScript, written by the people behind Firefox. - SQLBolt (SQLBolt)
Short interactive lessons in SQL that run in the browser: selecting, filtering, joining, and grouping. Useful for CMSC 225 and for any job that touches a database. - The Missing Semester of Your CS Education (MIT)
Short lectures on the tools courses assume you know: the command line, text editors, Git, debugging, and scripting.
Data, spreadsheets, and code
I need Excel, R, or Python for a class, a thesis, or a job, outside the data science and CS sequences. Free lessons and in-browser tools for getting a project done. No installation needed for most of these.
Start here: Excel, R, and Python
Stuck right now · 10 minutes. Search for the exact task or error message, such as "Excel VLOOKUP" or "R read csv." Then check the official help in Excel help and learning or R for Data Science (2e).
Behind on a topic · an evening. New to Excel? Start with Excel tutorials (GCFGlobal). For R, read the first chapters of R for Data Science (2e) in Posit Cloud, with nothing to install. For Python, use Python for Everybody in Google Colab.
Rebuilding a skill · a few weeks. Pick one tool and one small project with your own data. The Software Carpentry lessons lessons are built for exactly this.
Tip. Keep your raw data in its own untouched file, and do all your cleaning in a copy.
- ★ R for Data Science (2e) (Wickham, Çetinkaya-Rundel, and Grolemund)
The standard free introduction to doing data analysis in R with the tidyverse: importing, cleaning, visualizing, and summarizing data.
Start: The "Whole game" chapters get you to a working analysis fast. - ★ Python for Everybody (Charles Severance, University of Michigan)
A complete beginner's course in Python with a free textbook, video lectures, and auto-graded exercises. Assumes no programming background. - ★ Excel tutorials (GCFGlobal) (GCFGlobal / LearnFree)
Plain-language, step-by-step Excel lessons for complete beginners, with practice files. - Posit Cloud (Posit)
RStudio in a web browser, so you can run R without installing anything. - Google Colab (Google)
Python notebooks that run in the browser with common data libraries already installed. - SQLBolt (SQLBolt)
Short interactive lessons in SQL that run in the browser: selecting, filtering, joining, and grouping. Useful for CMSC 225 and for any job that touches a database. - Software Carpentry lessons (The Carpentries)
Short, tested lessons on the command line, version control with Git, and programming in Python or R, written for researchers. - Excel help and learning (Microsoft)
Microsoft's official tutorials and video training for Excel, from formulas and charts to PivotTables. Lawrence accounts include Microsoft 365.
Quantitative work in the sciences
The math in my physics, chemistry, or biology course is the problem. Units, equations, and models as they show up in science courses.
Start here: math in science courses
Stuck right now · 10 minutes. Check the units. Write every quantity with its units and see whether they combine into the units of the answer.
Behind on a topic · an evening. Work the matching module of The Math You Need, When You Need It (unit conversions, rearranging equations, logarithms). Look up the concept on HyperPhysics or Chemistry LibreTexts.
Rebuilding a skill · a few weeks. If algebra is the bottleneck, work through basics and algebra alongside your science course.
Tip. Solve the equation for the unknown before you plug in numbers. It's easier to check and to reuse.
- ★ HyperPhysics (Carl R. Nave, Georgia State University)
A linked concept map of introductory physics with formulas, diagrams, and worked calculations. Quick for looking up how one idea connects to another. - ★ The Math You Need, When You Need It (SERC, Carleton College)
Short modules on the math that intro science courses assume: unit conversions, rearranging equations, slopes, logarithms, and density, each with practice problems.
Start: Start with unit conversions and rearranging equations. - PhET Interactive Simulations (University of Colorado Boulder)
Research-based simulations in physics, chemistry, and math (graphing lines, quadratics, fractions, vectors). Good for building intuition before solving problems. - University Physics, Volumes 1–3 (OpenStax, Rice University)
A calculus-based introductory physics text. Each chapter has worked examples with a "strategy, solution, significance" structure. - Chemistry 2e (OpenStax, Rice University)
A general chemistry text. Its appendices on essential math (exponents, logarithms, significant figures) are useful on their own. - Chemistry LibreTexts (LibreTexts)
A large library of open chemistry texts and modules, from general chemistry through physical chemistry. Search for a topic rather than browsing. - SI units (National Institute of Standards and Technology)
The official reference for SI base units, derived units, and prefixes.
Quantitative work in economics and social science
I need the math behind economics, or real data for a project. Open economics texts and reliable public data sources.
Start here: math in economics
Stuck right now · 10 minutes. Sketch the graph. Most introductory economics problems are about a slope or the point where two lines cross.
Behind on a topic · an evening. Read the appendix on graphs in Principles of Economics 3e, then the matching chapter of The Economy 2.0 (CORE Econ).
Rebuilding a skill · a few weeks. Practice with real data: download a series from FRED economic data and chart it in Excel (help with Excel).
Tip. A rate that goes from 4% to 5% rose one percentage point, which is a 25% increase. Say which one you mean.
- ★ The Economy 2.0 (CORE Econ) (The CORE Team)
A free, data-driven introduction to economics developed by an international group of economists. Uses real data and models throughout. - ★ FRED economic data (Federal Reserve Bank of St. Louis)
Hundreds of thousands of economic time series (GDP, unemployment, inflation, interest rates) with instant graphs and downloads. - Principles of Economics 3e (OpenStax, Rice University)
A conventional principles text covering micro and macro. The appendix on using graphs in economics is a good refresher on slope and linear equations. - Our World in Data (Global Change Data Lab and University of Oxford)
Charts and downloadable data on health, population, energy, poverty, and more, each with its sources documented. Good for projects and for practicing reading graphs.
Graphing and computing tools
I want to graph something, check an answer, or explore an idea. Free calculators and math software. Check your course policy before using them on graded work.
Start here: graphing calculators
Stuck right now · 10 minutes. Open Desmos graphing calculator, type your function, and add sliders for the constants.
Behind on a topic · an evening. Use tools to check your work, not to replace it. Solve by hand, then confirm with Wolfram|Alpha or GeoGebra.
Tip. Follow your course's policy on which tools are allowed for graded work.
- ★ Desmos graphing calculator (Desmos Studio)
A fast, easy graphing calculator in the browser. Add sliders to see how changing a coefficient changes a graph.
Start: Type y = a x^2 + b x + c and add sliders for a, b, and c. - GeoGebra (GeoGebra)
Graphing, geometry, 3D, and computer algebra in one free tool, with thousands of ready-made activities. - Wolfram|Alpha (Wolfram Research)
Answers math questions typed in plain language: solves equations, simplifies, differentiates, integrates, and plots. Best for checking your work after you've done it.
How to study math
I put in the hours but it isn't sticking, or math makes me anxious. Research-based study strategies and resources on math anxiety and mindset.
Start here: studying and math anxiety
Stuck right now · 10 minutes. Try the 10-minute routine for when you're stuck.
Behind on a topic · an evening. Read the Six strategies for effective learning posters on retrieval practice and interleaving. Then test yourself on last week's material without notes.
Rebuilding a skill · a few weeks. Plan your next exam with the 10-day exam plan. If anxiety gets in the way, youcubed has good reading on math mindset, and a coach at the Center for Academic Success can help you make a plan.
Tip. Feeling anxious about math is common and doesn't mean you're bad at it. If anxiety is affecting more than math, campus counseling services can help.
- ★ Six strategies for effective learning (The Learning Scientists)
Posters, slides, and bookmarks on six research-backed strategies: spaced practice, retrieval practice, elaboration, interleaving, concrete examples, and dual coding.
Start: Read the retrieval practice and interleaving posters first; they matter most for math. - Common math errors (Paul Dawkins, Lamar University)
A short catalog of the algebra and calculus mistakes Paul Dawkins sees most often, each with the correct version. A good page to read the night before an exam. - Retrieval practice for students (Pooja K. Agarwal)
Short, research-based advice on studying by recalling and practicing instead of rereading. - youcubed (Stanford Graduate School of Education)
Resources on mathematical mindset and visual approaches to math. Helpful reading for students who believe they are "not a math person," and for the people who teach them.
Writing and presenting quantitative work
I have to write up math, make a chart, or present results. Typesetting, data visualization, and writing with numbers.
Start here: writing up math and making charts
Stuck right now · 10 minutes. For a chart, write the one sentence you want it to say, and use that sentence as its title.
Behind on a topic · an evening. To typeset math, work through Learn LaTeX in 30 minutes. For charts and posters, see the Communication handouts, including data visualization.
Rebuilding a skill · a few weeks. Read Quantitative writing on writing with numbers, and take a draft to writing tutoring (Course tutors through Navigate).
- ★ Learn LaTeX in 30 minutes (Overleaf)
The standard first tutorial for typesetting math with LaTeX in an online editor. The rest of Overleaf's documentation answers almost any later question. - Quantitative writing (SERC, Carleton College)
What it means to write with numbers, with tutorials and examples of quantitative writing assignments across disciplines. - Communication handouts, including data visualization (Carnegie Mellon University, Student Academic Success Center)
Printable handouts on scientific writing, presentations, research posters, tables and charts, and data visualization.
Beyond the course
I'm preparing for the GRE, or I want numbers to make sense in everyday life. Graduate admissions tests and quantitative reasoning for its own sake.
Start here: the GRE and everyday math
Behind on a topic · an evening. Take one free official practice test from Official GRE prep materials to see where you stand.
Rebuilding a skill · a few weeks. Review the topics you missed with Khan Academy, and bring problems to the QRC. For everyday numbers, the finance chapter of Contemporary Mathematics covers interest, loans, and budgets.
- ★ Official GRE prep materials (ETS)
Free official practice tests and a math review for the GRE quantitative section, from the test maker. - [Used at Lawrence] Contemporary Mathematics (OpenStax, Rice University)
A liberal-arts math text on sets, logic, probability, statistics, personal finance, and geometry. Good for quantitative reasoning outside a math major.
Start: The personal finance chapter covers interest, loans, and budgeting. - Math in Society (David Lippman)
Short chapters on voting, apportionment, finance, growth models, statistics, and graph theory as they come up in civic life.
Tutoring practice and training
I tutor (or want to) and want to get better at it. Standards and materials for peer tutors and the people who train them.
- ★ CRLA tutor training certification (ITTPC) (College Reading and Learning Association)
The standards the QRC trains to. Level 1 requires at least 10 hours of training on 8 topics and 25 hours of tutoring. Certification goes to programs, not individual tutors.
Start: Read the Level 1 topics list to see what your training covers. - QMaSC Handbook: training and mentoring chapters (Coulombe, O'Neill, and Schuckers, eds.)
Chapters 14 and 15 of this handbook collect training methods and practice scenarios written by directors of math and quantitative centers at peer colleges.
Start: Chapter 15, Practice and Mentoring, is a bank of tutoring scenarios.
Teaching quantitative reasoning
I teach a course with quantitative content, in any department. Free guides, activities, and open textbooks for faculty.
- ★ Developing quantitative reasoning (Nathan Grawe, SERC, Carleton College)
How to build quantitative reasoning into a course in any discipline: what QR is, principles for teaching it, designing assignments, and assessing them with rubrics. - ★ AIM approved open textbooks (American Institute of Mathematics)
A reviewed list of free math textbooks from precalculus through upper-division courses. Start here if you want to drop a commercial textbook. - MAA Instructional Practices Guide (Mathematical Association of America)
An evidence-based guide to classroom practices, assessment, and course design in college mathematics, with a companion book-study guide. - Teaching with Spreadsheets Across the Curriculum (SERC, Carleton College)
Ready-made modules in which students build Excel spreadsheets to answer questions in subjects from geology to economics.
Running a quantitative center
I support or plan quantitative learning at Lawrence. The professional literature on quantitative and math support centers.
- ★ QMaSC: A Handbook for Directors of Quantitative and Mathematics Support Centers (Coulombe, O'Neill, and Schuckers, eds. (2016))
The handbook for this field: management, outreach, faculty development, training, assessment, space design, and ten case studies of centers at colleges like Bates, Hamilton, Smith, and St. Lawrence.
Start: Chapters 9 (outreach) and 12 (virtual presence) shaped this directory. - Numeracy (journal) (National Numeracy Network)
The peer-reviewed, open-access journal on quantitative literacy across disciplines.