Michigan State University (MSU) Math Help & Mastery Lab | Calculus II: MTH 133/153H; Multivariable Calculus: MTH 234/254H; Differential Equations: MTH 235/340/347H/441; Linear Algebra: MTH 309/314/317H/414/415; Abstract Algebra: MTH 310/411/418H/419H; Real Analysis: MTH 320/327H/421/429H; Galois Theory: MTH 411/419H; Number Theory: MTH 310/417; Complex Analysis: MTH 425; PDEs: MTH 442; Numerical Analysis: MTH 451/452; Topology: MTH 461; Discrete Mathematics: MTH 481/482; Proofs: MTH 299

MTH 133: Calculus II combines integral techniques and applications with improper integrals, polar and parametric curves, and infinite series. MTH 153H: Honors Calculus II adds a stronger emphasis on concepts and theory, with Taylor series explicitly named in its description.

With Woody, work on the choices that slow you down: substitution or integration by parts? Washers or cylindrical shells? A comparison test or a ratio test? Draw the region, identify the structure, and explain the choice before carrying out the algebra.

For a power series, keep the radius calculation separate from the endpoint checks. Match the examples to your section’s syllabus, then practice mixed problems until you can begin without a hint.

MTH 234: Multivariable Calculus develops several-variable differentiation and integration, with vectors, line and surface integrals, and Green’s and Stokes’s theorems. MTH 254H: Honors Multivariable Calculus is the honors route.

A difficult triple integral often begins with a geometry problem. Identify the solid and its projections before setting bounds. For circulation or flux, state the curve or surface orientation and check a theorem’s hypotheses before using it.

Woody helps connect each calculation to what it measures. Bring the diagram, problem statement, and your attempted setup so the point of confusion is clear.

MTH 235: Differential Equations includes first-order and higher-order equations, Laplace transforms, linear systems, and introductory Fourier/PDE work. The official title is Differential Equations.

MTH 340: Ordinary Differential Equations I includes existence and uniqueness, qualitative reasoning, and Fourier applications. MTH 347H: Honors Ordinary Differential Equations places greater emphasis on theory. These courses have different requirements; match the support to your actual course and syllabus.

With Woody, identify order and linearity, choose a method, apply the initial conditions, and substitute your result back into the equation. Later work in MTH 441: Ordinary Differential Equations II brings stability and dynamical systems into focus.

MTH 309: Linear Algebra I emphasizes mathematical writing and proofs. MTH 314: Matrix Algebra with Computational Applications focuses on numerical matrix methods. MTH 317H: Honors Linear Algebra emphasizes concepts and rigorous reasoning. These are distinct routes, not one interchangeable course.

MTH 414: Linear Algebra II develops abstract vector spaces and operators. MTH 415: Applied Linear Algebra includes least squares, matrix decompositions, singular values, and Fourier methods.

Work with Woody on the reasoning behind elimination, bases, eigenvectors, and orthogonality. For a proof, name the space and transformation; for a computation, check dimensions and interpret the result.

MTH 310: Abstract Algebra I and Number Theory and MTH 411: Abstract Algebra II form the standard algebra route. MTH 418H: Honors Algebra I and MTH 419H: Honors Algebra II are the honors courses.

MSU’s Fall 2026 interim descriptions move group theory into the first course and place rings, fields, and introductory Galois theory in the second. Use your current syllabus rather than assuming an older topic list still applies.

With Woody, begin a proof by writing exactly what must be shown. Check closure, kernels, normality, or well-definedness where needed, and explain each use of a theorem. A useful example can guide the argument; the proof must cover the full claim.

MTH 320: Analysis I covers rigorous convergence, completeness, continuity, differentiation, and uniform convergence. MTH 421: Analysis II continues into Riemann integration, metric spaces, and higher-dimensional differentiation.

MTH 327H: Honors Introduction to Analysis and MTH 429H: Honors Real Analysis provide the honors route. Match your work to the definitions and theorem statements used in your section.

With Woody, make the logical structure visible: what is given, what must be chosen, and what estimate completes the proof? Distinguish pointwise from uniform convergence, test missing assumptions with counterexamples, and justify when a limit may pass through an integral or derivative.

MTH 419H: Honors Algebra II explicitly includes field extensions and Galois theory. The Fall 2026 interim description of MTH 411: Abstract Algebra II also introduces Galois theory after rings and fields.

Bring the exact exercise and the results your class has established. Work on irreducibility, minimal polynomials, extension degrees, splitting fields, and automorphisms in the order the problem requires.

With Woody, draw the field relationships and explain what an automorphism must fix. The goal is to see why a proposed group or intermediate field is correct, with the necessary hypotheses checked.

MTH 310: Abstract Algebra I and Number Theory supplies an introduction to integer structure and modular arithmetic. MTH 417: Topics in Number Theory reaches further into higher congruences, primitive roots, quadratic reciprocity, and number-theoretic functions.

Work with Woody on the decision behind the calculation. Does a modular inverse exist? Can a gcd condition settle solvability? Which theorem applies to the modulus you have?

For a proof, separate the example that suggests the idea from the argument that establishes it. State assumptions clearly and keep every congruence tied to its modulus.