Georgia Tech (GT) Math Help & Mastery Lab | Calculus II / Integral Calculus: MATH 1552; Multivariable Calculus: MATH 2550/2551/2561; Differential Equations: MATH 2552/2562; Linear Algebra: MATH 1553/1554/1564/3406/4305; Abstract Algebra & Galois Theory: MATH 4107/4108; Real Analysis: MATH 4317/4318; Number Theory: MATH 4150; Combinatorics: MATH 3012/4032; Complex Analysis: MATH 4320; PDEs: MATH 4347; Topology: MATH 4431; Mathematical Methods in Engineering: MATH 4581; Numerical Analysis & Differential Equations: MATH 4640/4641; Proofs: MATH 2106

MATH 1552: Integral Calculus combines integration, applications, improper integrals, and infinite series. Georgia Tech’s published outline also includes Taylor approximation and applications involving volume, arc length, work, and center of mass.

With Woody, practice the decision before the calculation: what suggests substitution, integration by parts, trigonometric substitution, or partial fractions? For volumes, draw the region and compare washers with cylindrical shells before writing bounds.

For series, identify the term structure, choose a test, and state what its result actually proves. Treat a power series’ radius and endpoint checks as separate tasks. Return to mixed practice until you can explain each first step aloud.

MATH 2551: Multivariable Calculus includes multivariable derivatives, constrained optimization, multiple integrals, and vector calculus through Green’s, Gauss’s, and Stokes’ theorems. MATH 2561: Honors Multivariable Calculus follows those subjects with greater depth and rigor.

MATH 2550: Introduction to Multivariable Calculus is a separate, shorter course. It includes several-variable differentiation and integration but does not cover vector calculus. Match your study plan to the course you are actually taking.

With Woody, sketch a solid before choosing Cartesian, cylindrical, or spherical coordinates. For a vector integral, identify the curve or surface, its orientation, and the hypotheses of any theorem you use. A correct setup should explain why the calculation answers the question.

MATH 2552: Differential Equations develops analytic and numerical solution methods with modeling applications. The School of Mathematics outline includes first-order equations, systems, second-order linear equations, Laplace transforms, nonlinear stability, and numerical approximation. MATH 2562: Honors Differential Equations treats the corresponding material more intensively.

With Woody, classify order and linearity, inspect the coefficients, and write down the conditions. Separate the homogeneous and particular parts, then substitute your answer into the original equation. For a system, connect eigenvalues and eigenvectors to the solution’s behavior.

For later engineering work, MATH 4581: Classical Mathematical Methods in Engineering connects Fourier and Laplace methods to boundary-value problems. MATH 4347: Partial Differential Equations I extends the discussion to equations involving several independent variables.

MATH 1553: Introduction to Linear Algebra is Georgia Tech’s shorter introductory course. MATH 1554: Linear Algebra offers a broader treatment, while MATH 1564: Linear Algebra with Abstract Vector Spaces emphasizes abstract spaces and transformations. These are different introductory routes, not three successive courses.

For further study, MATH 3406: A Second Course in Linear Algebra develops theory and applications, including operators and canonical forms. MATH 4305: Topics in Linear Algebra covers spaces, transformations, inner products, and related matrix methods.

With Woody, explain what each pivot says about a system. A basis argument must show both spanning and independence. For eigenvalue work, decide whether diagonalization is justified before using it. For a proof, name the space, field, and map so the argument has a clear starting point.

MATH 4107: Introduction to Abstract Algebra I emphasizes algebraic structures and proof. The School’s outline develops modular arithmetic, rings and polynomial rings, and group theory. MATH 4108: Introduction to Abstract Algebra II continues into more advanced algebra, including Galois theory and modules.

With Woody, unpack the definition before reaching for a theorem. To prove a map is an isomorphism, organize the required claims; to use a quotient, explain why the construction is valid. Work through concrete examples alongside the abstract statement.

MATH 2106: Foundations of Mathematical Proof provides a useful bridge into this work. Practice direct proof, contradiction, contrapositive, and induction with clear quantifiers and a stated goal.

MATH 4317: Analysis I studies the real-number foundation, Euclidean topology, sequences, continuity, and function convergence. MATH 4318: Analysis II continues with differentiation and integration, including the Riemann–Stieltjes integral and analysis in several real variables.

With Woody, begin a limit proof by writing what must be made small and what you may choose. Distinguish a pointwise statement from a uniform one. Before interchanging a limit with an integral or derivative, identify a theorem and verify its hypotheses.

Build a small collection of examples and counterexamples: a function that is continuous but not uniformly continuous, a convergent sequence with the behavior the theorem allows, or a missing assumption that makes a proposed proof fail. These examples make abstract statements easier to use.

Galois theory is an explicit part of MATH 4108: Introduction to Abstract Algebra II. It belongs within Georgia Tech’s second algebra course; it is not a separate undergraduate course number on this page.

With Woody, start by naming the base field and checking irreducibility where needed. Construct a splitting field carefully, compute degrees using justified steps, and describe which elements an automorphism can send to which roots.

When applying the Galois correspondence, keep the direction of containment clear and match each subgroup to its fixed field. Use a small worked example before moving to a more complicated polynomial. Bring your syllabus and attempted proof so the discussion matches your course’s treatment.

MATH 4150: Introduction to Number Theory covers prime factorization, congruences, integer equations, and related applications. Georgia Tech’s outline includes the Euclidean algorithm, the Chinese remainder theorem, quadratic residues, and cryptographic applications.

With Woody, translate an arithmetic question into a divisibility statement or congruence you can use. In a linear Diophantine equation, check the gcd condition before searching for solutions. In modular arithmetic, verify that an inverse exists before dividing.

For a theorem-based problem, write the hypotheses first. Then use a small example to test your reasoning and develop a proof that works for every permitted input. The aim is a complete argument, not a pattern that happened to work a few times.