Chapman University Math Tutor & Mastery Lab | Calculus II: MATH 111, MATH 116 (accelerated series); Calculus III & Vector Calculus: MATH 210, MATH 116 (accelerated); Differential Equations: MATH 215/350/351; Linear Algebra: MATH 211/215/315; Abstract Algebra: MATH 380/460; Real Analysis & Advanced Calculus: MATH 450; Galois Theory: field extensions & advanced support; Number Theory: MATH 260

MATH 111: Single Variable Calculus II is Chapman’s standard Calculus II course. The alternative MATH 116: Accelerated Calculus Part II: Series, Differential Equations and Multivariable Calculus combines several subjects in one course. Its series work connects to Calculus 2 support, while its later topics connect to the sections below.

For MATH 111, work with Woody on substitution, integration by parts, trigonometric methods, partial fractions, and applications. For a volume problem, compare washers and cylindrical shells: sketch the region, identify the radius and height, and explain the bounds before integrating. Those decisions are the skill you want to carry into the next exam.

For sequences and series, learn to distinguish a convergence question from an approximation question. Explain why a comparison, ratio test, alternating-series argument, or Taylor expansion fits. Use the Mastery Lab to study a complete example, reconstruct the reasoning, and test yourself on a new problem. Match the pace and topic order to your current Chapman syllabus.

MATH 210: Multivariable Calculus is the Chapman course for students moving beyond single-variable calculus. Multivariable work also appears within the accelerated MATH 116 route. These courses organize the material differently; bring your syllabus and current topic so the study plan fits your class.

Work with Woody on vectors, partial derivatives, gradients, constrained optimization, and multiple integrals. Start a region problem by drawing its boundaries. Before changing the order of integration or choosing polar, cylindrical, or spherical coordinates, explain how each bound describes the same region.

For vector calculus, connect a line or surface integral to the curve or surface itself. Identify orientation, then decide whether direct computation or a theorem offers the clearest path. Practice stating the conditions for Green’s, Stokes’s, or the divergence theorem as carefully as you perform the algebra. Your course syllabus determines which of these topics are included and when.

MATH 350: Differential Equations is Chapman’s dedicated differential-equations course. MATH 215: Introduction to Linear Algebra and Differential Equations combines matrix methods with ordinary differential equations. The introductory differential-equation component of MATH 116 is another starting point, with a different scope and pace.

Work with Woody on first-order methods, higher-order linear equations, systems, Laplace transforms, and series solutions as your syllabus requires. Identify the order and linearity, choose a method, apply the initial conditions, and substitute the result back into the original equation. For a model, define the quantities and units before solving.

MATH 351: Nonlinear Dynamics With Application to Science and Engineering is a related continuation for students studying nonlinear behavior. Bring the particular model or dynamical-system topic you are working on. The Mastery Lab gives you a place to rebuild the calculus and linear algebra behind that work and ask Woody about the step you cannot yet explain.

MATH 211: Linear Algebra and the combined MATH 215 route provide Chapman linear-algebra references. MATH 315: Linear Algebra II (Advanced Linear Algebra) develops the subject further. Linear algebra is a core Mastery Lab subject, with support matched to your preparation and current course.

When solving a system or reducing a matrix, connect each operation to its meaning. Identify the kernel and image, distinguish span from independence, and explain how a basis describes the entire space. For a linear transformation, separate the map from its matrix representation in a chosen basis.

For MATH 315, work on precise arguments about inner products, invariant subspaces, operators, and eigenstructure. Where your syllabus includes spectral theory, singular values, or canonical forms, connect the theorem’s hypotheses to the examples you compute. Reconstruct a proof in your own words and use a counterexample to understand what fails when an assumption is removed.

MATH 380: Introduction to Abstract Algebra introduces algebraic structures, including semigroups, monoids, and groups. MATH 460: Modern Algebra is another Chapman algebra course. Bring your current syllabus so the work matches the structures and theorems your section uses.

With Woody, begin by separating the assumptions from the conclusion. Test a definition on a small example, then turn that understanding into a proof. When studying a subgroup, homomorphism, or quotient, write the exact property that makes the next step valid.

In ring and field work, keep the ambient structure explicit: an argument valid over a field may fail over a general ring. Study a complete argument in the Mastery Lab, explain the reason for each step aloud, then reconstruct it and try a related problem. The aim is to recognize a proof strategy you can use again.

MATH 450: Real Analysis is Chapman’s advanced-calculus and real-analysis course. Its subject matter connects the real number system, sequences, series, and functions to the logical foundations behind calculus.

With Woody, start by translating a statement into a precise target. In an epsilon argument, identify what is given and what you must choose. For a sequence of functions, distinguish a bound that depends on the point from one that works throughout the domain.

Use carefully chosen examples to separate convergence, continuity, and uniform behavior. Before passing a limit through a sum, derivative, or integral, name the theorem and check its assumptions. Practice writing an argument that another reader can follow without guessing the missing steps, then test your understanding on a counterexample.

Galois theory support is available for Chapman students studying field extensions in advanced algebra or independent work. Bring the topic or reading you are using so Woody can help you build a focused plan.

Begin with irreducibility, minimal polynomials, and extension degrees. When adjoining roots, keep track of what the field already contains. For an automorphism, determine which images of a generator are possible and why those images preserve its algebraic relations.

Then connect subgroups with intermediate fields and check the conditions for applying the Galois correspondence. Work through a concrete splitting-field example before attempting the general proof.

MATH 260: Number Theory is Chapman’s number-theory course. It provides a setting for studying integers, divisibility, primes, and factorization while developing proof-based reasoning.

With Woody, connect the Euclidean algorithm to greatest common divisors and integer combinations. For a congruence, ask whether a factor is invertible before canceling it. Separate the existence of a solution from the description of every solution, especially in Diophantine equations.

When a theorem seems useful, state its hypotheses before applying it. Test small cases to discover a pattern, then use a direct argument, contradiction, or induction to establish the result. The Mastery Lab’s number-theory and algebra support can help you practice that transition from experimentation to proof.