Difference between revisions of "MATH 1564"
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| − | {{DISPLAYTITLE:MATH |
+ | {{DISPLAYTITLE:MATH 1564 - Linear Algebra with Abstract Vector Spaces}} |
| + | MATH 1564 covers linear algebra and abstract vector spaces. It is a core [[mathematics|math]] course worth 4 credit hours. |
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| − | MATH 2603 covers discrete mathematics, which is a sampling of topics from logic, set theory, algorithms, combinatorics, probability, and graph theory. It is a 4 credit hour course. |
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== Topic List == |
== Topic List == |
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| + | * Systems of equations |
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| − | * Logic |
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| + | * Geometry of vectors |
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| − | * Sets, relations, functions |
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| + | * Abstract vector spaces |
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| − | * Bijection and cardinality |
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| + | * Spanning, independence, and bases |
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| − | * Equivalence relations and partitions |
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| + | * Isomorphism and the Fundamental Theorem of Vector Spaces |
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| − | * Induction and recursion |
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| + | * Linear transformations, and the matrix of a transformation |
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| − | * Algorithms |
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| + | * Matrix operations |
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| − | * Combinatorics |
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| + | * Matrix and transformation inverses |
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| − | * Probability |
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| + | * Markov chains |
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| − | * Graphs |
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| + | * Change of basis |
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| − | * Trees |
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| + | * Orthogonal projection, Gram-Schmidt, line of best fit |
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| + | * Determinants |
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| + | * Complex vector spaces |
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| + | * Similarity, diagonalizability, eigenvalue and eigenvector |
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| + | * Page ranking |
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| + | * Jordan canonical form |
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== Prerequisite Knowledge == |
== Prerequisite Knowledge == |
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| + | Calculus with a high score. |
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| − | The GaTech math department formally requires having passed a calculus course. |
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| − | Calculus is used very little |
+ | Calculus is used very little in this course. The calculus prerequisite only shows that you are able to learn mathematics at this level. |
== Equivalent Courses == |
== Equivalent Courses == |
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| + | [[MATH 1553]] and [[MATH 1554]], each of which covers linear algebra but with less emphasis on abstraction. |
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| − | MATH 2602, titled "Linear and Discrete Mathematics". |
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| − | |||
| − | There is a large overlap with topics in [[CS 2050]], although this course focuses more heavily on number theory and topics related to computing. |
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== Resources == |
== Resources == |
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| − | * |
+ | * A textbook often used for this course is ''Linear Algebra'' by Hefferon. |
| − | * [https://www.youtube.com/playlist?list=PLcwjc2OQcM4t0iNqMka93HCM4I2HWyNgp A Course in Discrete Math] explains similar topics with worked exercises. |
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[[Category:Courses|^MATH^MATH]] |
[[Category:Courses|^MATH^MATH]] |
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Revision as of 12:04, 18 February 2025
MATH 1564 covers linear algebra and abstract vector spaces. It is a core math course worth 4 credit hours.
Topic List
- Systems of equations
- Geometry of vectors
- Abstract vector spaces
- Spanning, independence, and bases
- Isomorphism and the Fundamental Theorem of Vector Spaces
- Linear transformations, and the matrix of a transformation
- Matrix operations
- Matrix and transformation inverses
- Markov chains
- Change of basis
- Orthogonal projection, Gram-Schmidt, line of best fit
- Determinants
- Complex vector spaces
- Similarity, diagonalizability, eigenvalue and eigenvector
- Page ranking
- Jordan canonical form
Prerequisite Knowledge
Calculus with a high score.
Calculus is used very little in this course. The calculus prerequisite only shows that you are able to learn mathematics at this level.
Equivalent Courses
MATH 1553 and MATH 1554, each of which covers linear algebra but with less emphasis on abstraction.
Resources
- A textbook often used for this course is Linear Algebra by Hefferon.
