Arizona State University (ASU) Math Help & Mastery Lab | Calculus II: MAT 266/271; Calculus III: MAT 267/272; Differential Equations: MAT 274/275/475; Partial Differential Equations: MAT 476; Linear Algebra: MAT 342/343/442; Abstract Algebra: MAT 443/444; Galois Theory; Advanced Calculus & Real Analysis: MAT 371/372/472/473; Number Theory: MAT 445

MAT 266: Calculus for Engineers II and MAT 271: Calculus with Analytic Geometry II are ASU’s two main second-semester calculus options. Both involve integration and series, but your own syllabus determines the sequence, depth, and assessment expectations.

Build a decision process for substitution, integration by parts, trigonometric substitution, and partial fractions. For volumes by disks, washers, and cylindrical shells, start with the region and axis of rotation; explain the radius, height, thickness, and bounds before integrating.

Series require a different set of decisions. Identify the form, check the hypotheses of a convergence test, and state what your result establishes. Use the Lab to study a worked example, then return to a mixed set where the method is not named for you.

MAT 267: Calculus for Engineers III and MAT 272: Calculus with Analytic Geometry III extend your work into several variables. Bring your course number and current assignment so Woody can match the practice to the version you are taking.

Work on the translation between pictures and formulas: a direction becomes a unit vector, a solid becomes integration bounds, and a vector field must be interpreted along a path or across a surface. Partial derivatives and gradients become more useful when you can explain what they measure.

In the Lab, practice setting up a problem before evaluating it. When your section reaches vector-calculus theorems, identify the region, boundary, and orientation and check the theorem’s assumptions.

MAT 275: Modern Differential Equations combines solution methods, applications, and problem solving using MATLAB. ASU also lists MAT 274: Elementary Differential Equations. Bring your exact course so the support fits your assigned mathematical and computational work.

For first-order equations, distinguish a separable problem from a linear one before beginning. For higher-order work, organize the homogeneous solution, any particular solution, and the initial conditions. Check the final expression in the original problem.

For students beyond the introductory level, Woody also supports MAT 475: Differential Equations and MAT 476: Partial Differential Equations. Match advanced topics such as boundary-value problems, Fourier methods, and separation of variables to your current syllabus.

ASU lists MAT 342: Linear Algebra, MAT 343: Applied Linear Algebra, and MAT 442: Advanced Linear Algebra. The exact course matters: bring your assignment so the emphasis matches the calculations, applications, or proofs you need.

Start with the spaces and dimensions involved. For a linear system, explain existence and uniqueness. For a transformation, identify its domain, codomain, kernel, and image. For eigenvalue work, connect the algebra to the action of the map.

Linear algebra is a core part of Woody’s instruction. Use the Lab to strengthen these ideas for your current course and for later differential equations, engineering, data science, and abstract mathematics.

MAT 443: Introduction to Abstract Algebra and MAT 444: Intermediate Abstract Algebra are the main ASU course references here. Bring the definitions, notation, and theorem statements your instructor is using.

Begin with concrete examples. Identify the operation and the elements before claiming that a set is a group. Specify a map and verify its properties before applying a theorem about its kernel or image. Distinguish a subgroup from a normal subgroup and an ideal from an arbitrary subset of a ring.

Woody’s guidance focuses on the reasoning that holds the argument together. Study a complete proof, explain why each step is allowed, and then test that understanding on a new structure or a carefully chosen counterexample.

ASU offers MAT 371: Advanced Calculus I and MAT 372: Advanced Calculus II, as well as MAT 472: Intermediate Real Analysis I and MAT 473: Intermediate Real Analysis II. These are distinct course levels; the study plan should follow your assigned material.

Work on the decisions inside a proof: what must be made small, which quantity can be bounded, where a hypothesis is used, and why a proposed counterexample works. An epsilon argument becomes more manageable when you separate the estimate from the final choice.

Use the Lab to build fluency with limits, continuity, convergence, and rigorous calculus. Match work on metric spaces, sequences of functions, integration, and more advanced analysis to your current section rather than treating every topic as part of one introductory course.

Galois theory support is available through Woody’s advanced algebra instruction. An ASU MAT 444 course page includes an overview connecting fields, geometric constructions, and the quintic. The depth of Galois theory in a particular MAT 444 section depends on its syllabus.

Bring your assigned problem, whether you are meeting field extensions for the first time or studying Galois theory in more depth. Begin with irreducible and minimal polynomials, extension degree, and the tower law; then connect automorphisms with fixed fields.

Woody can help you work through splitting fields, normality, separability, and the hypotheses behind the fundamental theorem of Galois theory. The aim is to understand the connection between the field calculation and the group calculation.

MAT 445: Theory of Numbers is listed among ASU’s advanced mathematics courses. Use your syllabus and current problem set to choose the number-theory material you need in the Lab.

Practice moving between divisibility statements, equations in integers, and congruences. Before cancelling or using an inverse modulo an integer, check that the step is justified. When you use Fermat’s little theorem or Euler’s theorem, state the relevant primality or coprimality condition.

For a Diophantine equation, finding one solution is only a beginning. Explain the complete family, show that each proposed solution works, and justify why no other possibilities remain.