Stony Brook University Math Help & Mastery Lab | Calculus II: MAT 132, AMS 161; Calculus B/C: MAT 126/127; Calculus III: MAT 203/307, AMS 261; Differential Equations: MAT 303/308, AMS 361; Linear Algebra: MAT 211/310/315, AMS 210; Abstract Algebra & Galois Theory: MAT 313/314; Real Analysis: MAT 319/320/322/324; Applied Real & Complex Analysis: MAT 341/342; Number Theory: MAT 311; Dynamics: MAT 351; Topology & Geometry: MAT 364/464/362; Applied Algebra: MAT 312/AMS 351; Algorithms: MAT 373; Proofs: MAT 200/250; Combinatorics: AMS 301

MAT 132: Calculus II and AMS 161: Applied Calculus II are important Stony Brook routes through integration and series. The three-course sequence splits related work between MAT 126: Calculus B and MAT 127: Calculus C: integral calculus in 126, then series and differential-equation models in 127.

With Woody, identify the feature that suggests substitution, parts, partial fractions, or a convergence test. For volume problems, sketch the solid before choosing washers or shells. Rework mixed practice until you can explain the first step without relying on a chapter heading.

Bring your exact course and syllabus. AMS 161 includes applied modeling and Fourier-series material; the MAT and AMS topic order should not be treated as identical.

MAT 203: Calculus III with Applications and AMS 261: Applied Calculus III develop multivariable and vector calculus. MAT 307: Multivariable Calculus with Linear Algebra combines this material with a more intensive treatment of matrices and vector spaces.

With Woody, sketch the domain before writing an integral. Explain where your limits come from, what the integrand measures, and why a coordinate change helps. For vector-calculus problems, distinguish a line integral from flux and check the orientation before using a theorem.

MAT 307 students can also work on the linear-algebra ideas that support the calculation. Bring your course number so practice follows your route and the level of explanation your instructor expects.

MAT 303: Calculus IV with Applications is a differential-equations course. AMS 361: Applied Calculus IV: Differential Equations is the applied route. MAT 308: Differential Equations with Linear Algebra integrates ODE theory with determinants, eigenvectors, and diagonalization.

With Woody, separate the decision from the calculation: identify order, linearity, coefficients, and conditions before choosing a technique. Keep the homogeneous and particular solutions distinct, then test the final answer.

Prepare for systems, transforms, and series using your instructor’s actual problem types. MAT 303 includes Fourier series; AMS 361 also lists partial differential equations. MAT 308 puts greater emphasis on the theoretical connection between linear algebra and differential equations.

MAT 211: Introduction to Linear Algebra and AMS 210: Applied Linear Algebra build the matrix and vector-space foundation. MAT 310: Linear Algebra develops the theory further, while MAT 315: Advanced Linear Algebra is the intensive advanced-track alternative.

With Woody, connect each computation to a mathematical statement. Explain why a set spans, why vectors are independent, and what an eigenvector reveals about a transformation. A row-reduced matrix should lead to a clear description of the solution set.

For MAT 310 or 315, practice complete arguments about linear maps, inner products, and canonical forms. MAT 315 also extends into quotient spaces and multilinear ideas. Bring your syllabus and proof attempt to match the work to your course.

MAT 313: Abstract Algebra develops groups, rings, homomorphisms, quotients, and fields. MAT 314: Abstract Algebra II continues through modules, field extensions, and Galois theory. MAT 312 / AMS 351: Applied Algebra connects algebraic structure with topics such as coding and modular arithmetic.

With Woody, unpack the definition before reaching for a theorem. Test proposed statements on concrete groups or rings, distinguish a subgroup from an ideal, and explain why a quotient construction is well-defined.

Bring your assigned theorem list so your solution uses the tools available in your class. If proof writing is the obstacle, the logic and set-language skills developed in MAT 200 and MAT 250 can be reviewed alongside your current algebra.

MAT 319: Foundations of Analysis and MAT 320: Introduction to Analysis build rigorous one-variable reasoning. MAT 322: Analysis in Several Dimensions develops multivariable theory. MAT 324: Real Analysis moves into Lebesgue measure, integration, and function spaces.

With Woody, translate a definition into the exact statement your proof must establish. Identify which quantities depend on others before choosing an estimate. Use counterexamples to test whether a hypothesis can be removed.

Match the practice to your level: an epsilon argument in MAT 319/320, an inverse-function argument in MAT 322, or a measure-and-integration question in MAT 324. Work toward explanations you can reproduce independently rather than a collection of proofs learned by appearance.

MAT 314: Abstract Algebra II explicitly includes an introduction to Galois theory, alongside modules and the theory of fields and field extensions.

With Woody, start by naming the base field and polynomial. Establish irreducibility before using it to determine a degree. When describing automorphisms, explain which choices preserve the algebraic relations.

Build field diagrams one justified inclusion at a time. Check the conditions needed for the correspondence between subgroups and intermediate fields, then connect the picture to the original equation. Bring your current theorem list and attempted solution so the explanation fits your instructor’s treatment.

MAT 311: Number Theory covers arithmetic questions involving congruences, quadratic residues, Diophantine equations, continued fractions, and primes. The department’s individual course page also labels it Introduction to Number Theory.

With Woody, decide whether a divisibility argument, modular calculation, or contradiction gives the cleanest path. Check coprimality before taking a modular inverse and explain the hypothesis of each theorem you use.

Small examples can suggest a pattern; the final proof must establish it for the entire stated class of integers. Bring the exact question and your attempt so work focuses on the missing reasoning. Connect number-theory methods to your algebra background when groups, rings, or polynomial structure provide a better explanation.