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4.2. Algebra and Number Theory (ANT)
Structural properties of mathematical systems including linear systems, abstract algebraic structures, and properties of integers.
| Knowledge Area (KA) | Core Tier1 | Core Tier2 |
 4.2.1 Matrices and Systems of Linear Equations | 1 | 1 |
|
4.2.2 Vector Spaces and Linear Transformations | 1 | 1 |
|
4.2.3 Eigenvalues and Inner Product Spaces | 1 | 1 |
4.2.1. ANT/Matrices and Systems of Linear Equations (Core Tier1: 1 hr, Core Tier2: 1 hr) ↑ Back to top
Matrix factorization and solution of engineering linear systems via LU, QR, Cholesky, and SVD decompositions.
Topics:
Core
- LU, QR, and Cholesky factorizations for solving engineering linear systems
- Singular Value Decomposition (SVD) and least squares solutions
Learning Outcomes:
Core:
- Solve systems of linear equations arising in structural, circuit, and fluid engineering problems [Usage]
- Apply the SVD to solve over-determined systems in data fitting and signal processing [Usage]
4.2.2. ANT/Vector Spaces and Linear Transformations (Core Tier1: 1 hr, Core Tier2: 1 hr) ↑ Back to top
Vector spaces and linear transformations with applications to engineering coordinate changes.
Topics:
Core
- Vector spaces, subspaces, bases, and dimension
- Linear transformations and their matrix representations in coordinate changes
Learning Outcomes:
Core:
- Formulate and interpret coordinate system transformations for engineering geometry problems [Assessment]
4.2.3. ANT/Eigenvalues and Inner Product Spaces (Core Tier1: 1 hr, Core Tier2: 1 hr) ↑ Back to top
Eigenvalues, diagonalization, and inner product spaces with applications to modal analysis of structures.
Topics:
Core
- Eigenvalues, eigenvectors, and diagonalization with applications to vibration and stability
- Inner product spaces, orthogonality, and the Gram-Schmidt process
Learning Outcomes:
Core:
- Perform eigenvalue decomposition on symmetric matrices for modal analysis of mechanical structures [Assessment]