UW–Madison mathematics.
Master the method.
Start with 7 days free in the Woody Calculus Mastery Lab.
Learn with a UW–Madison Pure Mathematics graduate. Video lessons, complete worked solutions, and direct guidance from Woody—backed by 25+ years teaching university mathematics.
7 days free, then $89/month. Private one-on-one sessions are separate.
Look inside the Mastery Lab
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Mathematics support for UW–Madison
From MATH 222 to Modern Algebra and Analysis: find your subject, then build a study plan inside the Mastery Lab.
- Calculus IIIntegration, applications, and infinite series
- Calculus IIISeveral variables, geometry, and vector calculus
- Differential EquationsEquations, systems, and method selection
- Linear AlgebraMatrices, vector spaces, and transformations
- Abstract AlgebraGroups, rings, fields, and proofs
- Real AnalysisLimits, convergence, and rigorous reasoning
- Galois TheoryField extensions and polynomial symmetry
- Number TheoryDivisibility, congruences, and proofs
Start with the work in front of you. Bring your UW course number, syllabus, and current topic. Woody can help you connect them to the relevant lessons and practice.
Look inside the Mastery Lab.
See the classrooms, video lessons, worked solutions, and community with Woody. Use your trial to explore the subject library that matches your Wisconsin course and ask where to begin.
Watch on YouTube if the player does not load
See every step.
Video classrooms and complete worked homework and exam solutions show how to begin, choose a method, and finish.
Ask Woody.
Get direct chat guidance, community support, and live Q&A when available. Bring the step you cannot explain.
Build independence.
Train pattern recognition, clean setup, formula fluency, and proof writing through structured practice.
Explore the lessons, study a worked solution, and bring Woody your next question.
7 days free, then $89/month.
From Beloit to Mifflin Street.
Still a Badger.
“This page is a personal one for me. I am a proud Badger.”
I was born and raised in Beloit, Wisconsin. After serving in the Army, I came to Madison, lived on Mifflin Street, and earned my undergraduate degree in Pure Mathematics at UW–Madison.
Madison is part of my own mathematics story. I know the city, the culture, and how demanding the transition from calculus to advanced mathematics can be.
Today, I bring 25+ years of university teaching experience to the students I work with through Woody Calculus. The Mastery Lab is where I teach the system: recognize the structure, choose the method, and work through the reasoning until you can do it independently.
Woody
UW–Madison alumnus · Founder, Woody Calculus
Work with a fellow Badger
- Calculus: decide which integration technique, series test, or multivariable setup fits.
- Differential equations: classify the equation before choosing the solution method.
- Linear and abstract algebra: connect calculations to definitions and structure.
- Analysis and proofs: name the hypotheses, organize the argument, and justify each step.
Woody is a UW–Madison alumnus. Woody Calculus is an independent education service and is not affiliated with, sponsored by, or endorsed by the university.
From integration to abstract proofs.
Find the method behind the work.
Match your UW–Madison course to the relevant subject below. The Lab connects professor-led explanations, worked solutions, practice, and guidance with the decisions your coursework asks you to make.
Calculus II
An integration problem and a convergence problem require different decisions. Build a study routine that makes you explain the choice before carrying out the calculation.
With Woody: Read the structure, choose the method, and finish with a check.
Course details and topics
MATH 222: Calculus and Analytic Geometry 2 brings integration techniques and infinite series into the same course. Your practice should build both skills: recognizing an integral’s form and deciding which convergence test has useful hypotheses.
Use the Mastery Lab to work through a complete example, then solve a related problem without looking. For applications involving volumes by disks, washers, and cylindrical shells, draw the region and axis of rotation before choosing a formula. First-order differential equations and vector geometry also appear in MATH 222; use your syllabus to keep the study plan aligned with your section.
- Substitution, integration by parts, trigonometric substitution, and partial fractions
- Improper integrals and convergence
- Volumes by disks, washers, and cylindrical shells
- Sequences, infinite series, and choosing convergence tests
- Power series; Taylor and Maclaurin series
- First-order differential equations and introductory vector geometry
UW–Madison calculus course overview UW–Madison MATH 222 course guide
Calculus III & Multivariable Calculus
A multiple integral becomes more manageable when the region is clear. Connect the picture, the coordinates, and the bounds before you begin calculating.
With Woody: Describe the geometry first; let that description guide the mathematics.
Course details and topics
MATH 234: Calculus—Functions of Several Variables is UW–Madison’s standard multivariable calculus course. It connects derivatives and integrals to curves, surfaces, regions, and vector fields.
In the Lab, practice the decisions that often cause difficulty: distinguishing a scalar function from a vector field, choosing a useful parametrization, finding integration bounds, and keeping track of orientation. A worked solution should explain why the setup matches the question, not simply display the final integral.
- Parametrized curves, vectors, and motion in space
- Partial derivatives, gradients, and directional derivatives
- Tangent planes and optimization in several variables
- Double and triple integrals with appropriate bounds and coordinates
- Vector fields, line integrals, and surface integrals
- Green’s theorem, Stokes’ theorem, and the divergence theorem
UW–Madison calculus course overview UW–Madison MATH 234 course guide
Differential Equations
Know whether the problem calls for a first-order method, a higher-order technique, a transform, or a system of equations. Then verify the solution you produce.
With Woody: Classify the equation, follow the method, and check the original conditions.
Course details and topics
MATH 319: Techniques in Ordinary Differential Equations concentrates on differential equations. MATH 320: Linear Algebra and Differential Equations combines the subjects, so matrix ideas need to become part of your solution process.
Bring your course number and current assignment into the Lab. For MATH 319, work on organizing the different ODE methods. For MATH 320, also connect eigenvalues and eigenvectors to systems and their behavior. These courses overlap, but your section’s syllabus determines the right practice.
When your work extends into mathematical methods, Woody also supports related Fourier-series, Laplace-transform, and partial-differential-equation topics. Start with the problem you need to understand.
- First-order equations and initial-value problems
- Homogeneous and nonhomogeneous linear equations
- Laplace transforms and inverse transforms
- Series solutions and boundary-value problems in MATH 319
- Matrix methods and linear systems in MATH 320
- Numerical or qualitative methods as included in your syllabus
- Checking the equation, initial conditions, and physical interpretation
UW–Madison differential equations course comparison UW–Madison mathematics course guide
Linear Algebra
Row reduction is one tool. Learn what it reveals about independence, a basis, a linear transformation, or the solutions of a system.
With Woody: Connect every calculation to a statement about the underlying space or map.
Course details and topics
MATH 340: Elementary Matrix and Linear Algebra and MATH 341: Linear Algebra call for related knowledge with different emphases. MATH 340 emphasizes matrix computation; MATH 341 places greater weight on proof writing.
Use the Lab’s Linear Algebra resources to build accurate calculations and clear explanations. If you are in MATH 341, practice turning a definition into a proof: identify the object, state what must be checked, and justify the conclusion. If you are in MATH 320, connect the same matrix ideas to your differential-equation systems.
Linear algebra is a core area of Woody’s instruction, with connections to engineering, physics, computer science, data science, and later pure mathematics.
- Linear systems, row reduction, and matrix operations
- Vector spaces, subspaces, linear independence, and span
- Bases, dimension, kernels, and images
- Linear transformations and their matrix representations
- Determinants, eigenvalues, eigenvectors, and diagonalization
- Proofs about spaces and maps, especially for MATH 341
UW–Madison linear algebra course comparison UW–Madison introduction to proof courses
Abstract Algebra
Build an argument from the objects in front of you. A familiar example can reveal the structure; a careful proof shows which parts of the example generalize.
With Woody: Name the structure, check the hypotheses, and explain each implication.
Course details and topics
MATH 541: Modern Algebra 1 and MATH 542: Modern Algebra 2 are UW–Madison’s modern-algebra sequence. Woody’s own undergraduate background in pure mathematics at UW gives this part of the page a personal connection.
For MATH 541, work carefully with groups, rings, ideals, homomorphisms, and quotient constructions. For MATH 542, connect polynomial and field questions to extensions and the algebraic structures on your syllabus.
Use the Lab to strengthen the step between understanding a definition and using it. Explain what a kernel contains, why an ideal has the required properties, or how an isomorphism is defined and verified. That precision is what makes a proof convincing.
- Groups, subgroups, normal subgroups, and quotient groups
- Homomorphisms, kernels, and isomorphism theorems
- Rings, ideals, integral domains, and polynomial rings
- Irreducibility, field extensions, and splitting fields
- Linear transformations and canonical forms where assigned
- Direct proofs, contradiction, examples, and counterexamples
Real Analysis
Learn to turn “this gets close” into a precise statement about limits. Quantifiers, estimates, and theorem hypotheses should each have a clear role in your argument.
With Woody: Write what is given, what must be proved, and the estimate that connects them.
Course details and topics
MATH 421: The Theory of Single Variable Calculus provides an introduction to proof through calculus. MATH 521: Analysis I and MATH 522: Analysis II carry analysis into the advanced sequence.
Woody helps you slow down the reasoning at the points that matter: choosing a useful bound, distinguishing pointwise from uniform convergence, checking completeness or compactness assumptions, and understanding why a theorem applies.
Bring the exact definition used in your course. Practice writing a complete argument, then test your understanding by changing a hypothesis or finding a counterexample. The aim is to explain the mathematics independently, in the language your course expects.
- Definitions, quantifiers, and epsilon-style arguments
- Sequences, series, limits, and continuity
- Metric-space ideas and basic topology as assigned
- Rigorous differentiation and integration
- Sequences and series of functions; uniform convergence
- Proof construction, estimates, and counterexamples
UW–Madison introduction to proof courses UW–Madison analysis course guide
Galois Theory
Make the relationship between fields and groups concrete. Start with a polynomial, identify its roots and extension, and determine the symmetries that preserve the base field.
With Woody: Track the extension, its automorphisms, and the elements each subgroup fixes.
Course details and topics
MATH 542: Modern Algebra 2 explicitly includes Galois-theory learning outcomes. This is support for the field-theory part of the algebra sequence, not a separate UW course number.
Build a reliable foundation in irreducibility, minimal polynomials, adjoining roots, and extension degree. Then work through explicit examples of automorphisms and fixed fields before applying the Galois correspondence. Woody’s guidance connects each calculation to the relevant definition, so the correspondence has a mathematical meaning beyond the diagram.
Use your instructor’s syllabus and assigned problems to choose the right depth of field theory and solvability questions.
- Irreducible and minimal polynomials
- Field extensions, bases, degrees, and the tower law
- Splitting fields and algebraic elements
- Field automorphisms, Galois groups, and fixed fields
- The fundamental theorem of Galois theory
- Polynomial solvability questions at your course’s level
Number Theory
An arithmetic pattern is a starting point. Learn to turn it into a proof using divisibility, congruences, and the precise conditions of the theorem you choose.
With Woody: Translate the claim into arithmetic structure, then prove each step.
Course details and topics
MATH 467: Introduction to Number Theory combines number theory with the development of proof-writing skills. It is a useful place to strengthen the transition from calculation to argument.
Use Woody’s Number Theory resources to practice a complete chain of reasoning: write divisibility statements correctly, handle congruences carefully, and explain why a result applies. When a statement is false, learn to construct a counterexample that directly addresses it.
Small numerical examples help you explore a claim. Your finished solution should show why it holds for every integer covered by the hypotheses.
- Divisibility, greatest common divisors, and the Euclidean algorithm
- Primes and integer factorization
- Congruences and modular arithmetic
- Fermat’s little theorem and its hypotheses
- Direct proof, contradiction, and mathematical induction
- Constructing examples and counterexamples
UW–Madison number theory as an introduction to proof UW–Madison MATH 467 course guide
Beyond the core sequence.
MATH 475: Introduction to Combinatorics brings counting and discrete proof techniques into the advanced-mathematics picture. Bring questions in combinatorics, advanced engineering mathematics, mathematical methods for physics, Fourier series, Laplace transforms, partial differential equations, and related proof-based work. These subjects draw on the calculus, differential equations, algebra, and analysis at the heart of Woody’s teaching.
Course names and numbers checked against the UW–Madison Department of Mathematics and the university’s mathematics course guide in September 2026. Your current syllabus determines the topics, pacing, and expectations for your section.
Make progress on this week’s topic.
Study a worked example, practice the method, and ask your next question.
Recognize the pattern.
Choose the method.
Do the work.
Fast-moving lectures and approaching exams can turn studying into a rush for answers. The Lab gives you a way to slow down the decisions that matter, then practice until you can make them independently.
Build clean setup, formula fluency, and complete reasoning alongside your calculations. The same habits support an integration problem, a matrix computation, or a proof.
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Bring your current UW–Madison work.
Start with your MATH course number, syllabus, homework topic, and next exam date. Choose the relevant subject library and show Woody what you are working on.
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Find the structure before the formula.
An integration-by-parts problem in MATH 222? A coordinate choice in MATH 234? A linear equation in MATH 319? Name the problem type before choosing the technique.
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Rebuild the complete reasoning.
Study a fully worked solution, rewrite it 3–5 times, and say the steps aloud. In a proof, state the definitions and theorem hypotheses as carefully as you explain an algebraic step.
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Practice without the solution in view.
Try a fresh problem. Check your calculation or proof, find the first step you cannot justify, and bring that precise question back to Woody.
Make your first week count.
Start with your current Wisconsin topic.
Open the subject library that matches your course, study a complete solution, and ask Woody about the step that is holding you back.
- Find your subject. Begin with the calculus, differential equations, linear algebra, or proof-based library that fits your current work.
- Study one complete solution. Follow the setup, method choice, calculations, and checks.
- Ask a focused question. Share your attempt and the first step you cannot explain.
- Try a related problem independently. Use the method and decide what to practice next.
7 days free, then $89/month. Private sessions are separate.
Private instruction for UW–Madison students.
Work one-on-one with a fellow Badger, backed by 25+ years teaching university mathematics. Woody helps Wisconsin students build a systematic approach to calculus, differential equations, algebra, analysis, and advanced proofs.
Get weekly one-on-one guidance, personalized exam strategy, detailed feedback, and accountability for your course.
Begin in the Mastery Lab. Students in Calculus II, Calculus III, Differential Equations, Linear Algebra, Abstract Algebra, Real Analysis, Galois Theory, Number Theory, and related advanced courses may then apply for individual instruction.
Private sessions are separate from membership and carry a premium fee. Availability is limited, application and approval are required, and Lab enrollment does not guarantee a private place.
- Join the Mastery Lab.
- Bring your course and goals.
- Apply for weekly private sessions.
Already a Lab member? Read the private instruction details.
Know what you are joining.
Did Woody attend UW–Madison?
Yes. Woody earned his undergraduate degree in Pure Mathematics at the University of Wisconsin–Madison. He grew up in Beloit, served in the Army, and lived on Mifflin Street while in Madison. His 25+ years of university teaching experience spans his broader career.
Where should I begin with MATH 222 or MATH 234?
Start in the Calculus II library for MATH 222 or the Calculus III library for MATH 234. Share your syllabus and current assignment with Woody so the recommended lessons match your section’s topics and pacing.
Can I get help with MATH 319 and MATH 320?
Yes. Bring the exact course and current topic. MATH 319 emphasizes techniques in ordinary differential equations; MATH 320 combines linear algebra and differential equations. The relevant libraries and guidance help you connect the methods to your own coursework.
Does the Lab support Modern Algebra and Analysis?
Yes. The teaching portfolio includes Abstract Algebra, Galois Theory, Real Analysis, Linear Algebra, Number Theory, and related advanced mathematics. Bring your definitions, theorem statements, and proof attempts so the guidance fits your course.
Can the Lab help me prepare for a UW midterm or final?
Use your instructor’s current review sheet and homework as the roadmap. Study complete examples, practice choosing methods, and solve fresh problems independently. Bring questions about the decisions or proof steps that still need work.
Can I ask Woody questions during the trial?
Yes. Membership includes direct chat guidance and community support, with live Q&A when available. Share the problem, what you tried, and the step you want explained.
What happens after the seven-day free trial?
Membership is $89 per month after the 7-day free trial. Review the membership terms on Skool when you join. Private one-on-one sessions are a separate service with a premium fee.
Are private sessions included in Lab membership?
No. Start in the Mastery Lab, then apply if you want weekly individual instruction. Private sessions require a separate premium fee, available space, and approval. Membership does not guarantee a private place.
Is Woody Calculus affiliated with UW–Madison?
No. Woody is an alumnus, and Woody Calculus is an independent education service. It is not affiliated with, sponsored by, or endorsed by the University of Wisconsin–Madison. Course references identify the students and subjects served.
Strengthen your first-semester foundations.
MATH 221: Calculus and Analytic Geometry 1 prepares students for MATH 222. Revisit limits, continuity, derivative rules, optimization, related rates, curve sketching, and beginning integration when those tools interrupt your progress.
Woody’s current private instruction focuses on Calculus II and above. Use the Calculus I foundations resources to review prerequisites.
Need private tutoring through Calculus I?
Woody recommends his longtime colleague Blue Hovatter for college algebra, precalculus, and Calculus I.
Go deeper into the mathematics.
Use these visual lessons and essays to connect the ideas behind your UW–Madison coursework.
Calculus IIGabriel’s Horn: Finite Volume, Infinite Surface AreaRead the essay
Multivariable calculusLine Integrals and Vector FieldsRead the essay
Differential equations & physicsFourier Series: Harmonics, Sound, Heat, and Quantum MechanicsRead the essay
Real analysisThe Cantor Set: Infinite Points, Zero LengthRead the essay
Abstract algebraGalois Theory: Hidden Symmetry and the QuinticRead the essay
Learn the method.
Put it to work at Wisconsin.
Begin with your current course. Study a complete solution, practice the reasoning, and bring Woody your next question. Your first seven days in the Mastery Lab are free.
7 days free, then $89/month.