Difference between revisions of "MATH 1554"

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{{DISPLAYTITLE:MATH 1554 - Linear Algebra}}
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== Overview ==
  
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'''MATH 1554''' covers linear systems, matrices, eigenvalues, orthogonality, and SVD.
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[https://math.gatech.edu/courses/math/1554 Course page]
  
   
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==== Topic List ====
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==Topic List ==
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*Linear Systems and Transformations
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MATH 1554 is basically just [[MATH 1553 - Introduction to Linear Algebra|MATH 1553]] but with an extra set of chapters (denoted with a *).
  
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** Systems of Linear Equations
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** Row Reduction and Echelon Forms
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** Vector Equations
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** The Matrix Equation
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** Solution Sets of Linear Systems
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** Linear Independence
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** Linear Transforms
   
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*Matrices and the Matrix Inverse
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# Systems of Linear Equations
  
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** Matrix Operations
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# Vectors in Rn
  
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** Matrix Inverse
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# Linear Independence and Transformations
  
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# Matrix Algebra
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** Invertible Matrix Theorem
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** Partitioned Matrices*
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# Subspaces in Rn
  
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** LU Factorization
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# Determinants
  
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** Leontief Input-Output Model*
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# Markov Chains (*)
  
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** Computer Graphics*
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# Eigenvalues and Eigenvectors
  
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** Subspaces
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# Complex Eigenvalues (*)
  
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** Dimension and Rank
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# PageRank (*)
  
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# Orthogonality
  
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# Symmetric Matrices
  
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# Quadratic Forms (*)
  
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# Singular Value Decomposition (*)
  
   
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*Determinants and Eigenvalues
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==== How it fits in the curriculum ====
  
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** Determinants
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Linear Algebra doesn't use any calculus, making it different from intro courses such as MATH 1551 and MATH 1552. This does mean that you can take MATH 1554 without any calculus credit.
 
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** Volume and Linear Transforms*
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** Markov Chains*
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** Eigenvalues and Eigenvectors
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** Characteristic Equation
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** Diagonalization
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** Complex Eigenvalues*
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** Google PageRank*
   
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*Orthogonality
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However, future calculus classes like Multivariable Calculus (MATH 2550/2551) and Differential Equations (MATH 2552) will use Linear Algebra concepts such as matrices, determinants, eigenvalues, characteristic equations, etc. Additionally, Linear Algebra is important for math classes required for CS such as Applied Combinatorics (MATH 3012) and Algorithms (CS 3510)
  
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** Inner Products
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** Orthogonal Sets
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** Orthogonal Projections
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** The Gram-Schmidt Process
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** Least-Squares
   
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*Symmetric Matrices, Quadratic Forms, and SVD
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== Current Registration Info ==
  
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** Symmetric Matrices
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This is a [[linked course]]. You must register for a lecture section (e.g. A, B, C) ''and'' a corresponding studio section with the same letter (e.g. lecture section A will have studio section A01, A02, etc.).
  
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** Quadratic Forms
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** Constrained Optimization*
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** Singular Value Decomposition (SVD)*
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<nowiki>*</nowiki> Topic not covered in [[MATH 1553]]
   
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== Class Structure ==
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For the lecture sections, notice how they all include one time-block very late in the day. This is likely the [[test period]], which will only meet a few times per semester. [TODO some1 confirm]
  
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MATH 1554 is a core math class with a focus on theory. However, MATH 1554 does ''not'' use formal proofs, and it still does have many computational problems. The theoretical nature of MATH 1554 can be challenging for first-year students who are used to more computation-heavy algebra and calculus courses.
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== Prerequisite Knowledge==
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If you enjoy theoretical math and proofs a lot, and consider yourself very good at math, consider MATH 1564.
 
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Almost no prerequisite knowledge is required, apart from algebra and trigonometry.
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==Scheduling==
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=== [https://oscar.gatech.edu/bprod/bwckctlg.p_disp_course_detail?cat_term_in=202108&subj_code_in=MATH&crse_numb_in=1554 Prerequisites] ===
  
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MATH 1554 is required for math and [[cs]] majors. Due to having almost no prerequisites, MATH 1554 is generally taken during freshmen year. Future calculus classes, such as [[Multivariable Calculus|multivariable calculus]] and [[Differential Equations|differential equations]] will use linear algebra concepts such as matrices, determinants, and eigenvalues. In addition, linear algebra is especially important for cs majors, who take many classes that require linear algebra, such as [[MATH 3012]] and [[CS 3510]].
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At least one of the following:
  
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* D or higher in MATH 1113 (Precalculus).
  
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* D or higher in MATH 1552 (Integral Calculus) or equivalent.
  
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* 620 or higher on the Math section of the SAT
  
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* 26 or higher on the Math section of the ACT.
  
   
 
=== Equivalent Courses ===
  
=== Equivalent Courses ===
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*MATH 1553 is the introduction equivalent, which does not cover as many topics as MATH 1554.
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MATH 1564
  
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*[[MATH 1564]] is the honors equivalent, which uses proofs and is more theoretical than MATH 1554.
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=== Majors That Require This Class ===
  
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* Applied Physics
  
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* Computational Media
  
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* Computer Engineering
  
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* Computer Science
  
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* Earth and Atmospheric Sciences
  
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* Electrical Engineering
  
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* Mathematics
  
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* Physics
  
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== Resources ==
  
== Resources ==
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* https://gatech.instructure.com/courses/114544 provides a set of videos and old exams for MATH 1554.
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[https://textbooks.math.gatech.edu/ila/1553/ <nowiki>Interactive Linear Algebra [1553]</nowiki>]
  
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*[https://textbooks.math.gatech.edu/ila/index.html Interactive Linear Algebra] is a free online, interactive textbook made by Georgia Tech professors. Although the textbook is intended for MATH 1553, it is still useful due to the similarity in concepts between MATH 1553 and 1554.
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*[https://www.3blue1brown.com/essence-of-linear-algebra-page 3blue1brown Essence of Linear Algebra Video Series] provides a nice conceptual overview of linear algebra. The video series uses visuals and animations extensively.
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A free online, interactive textbook made by Georgia Tech professors. It's for MATH 1553, but it covers most of the concepts for MATH 1554.
  
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[[Category:Courses|^MATH^MATH]]
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[https://www.3blue1brown.com/essence-of-linear-algebra-page 3blue1brown Essence of Linear Algebra Video Series]
  

Latest revision as of 22:56, 10 March 2022

MATH 1554 covers linear systems, matrices, eigenvalues, orthogonality, and SVD.

Topic List[edit | edit source]

  • Linear Systems and Transformations
    • Systems of Linear Equations
    • Row Reduction and Echelon Forms
    • Vector Equations
    • The Matrix Equation
    • Solution Sets of Linear Systems
    • Linear Independence
    • Linear Transforms
  • Matrices and the Matrix Inverse
    • Matrix Operations
    • Matrix Inverse
    • Invertible Matrix Theorem
    • Partitioned Matrices*
    • LU Factorization
    • Leontief Input-Output Model*
    • Computer Graphics*
    • Subspaces
    • Dimension and Rank
  • Determinants and Eigenvalues
    • Determinants
    • Volume and Linear Transforms*
    • Markov Chains*
    • Eigenvalues and Eigenvectors
    • Characteristic Equation
    • Diagonalization
    • Complex Eigenvalues*
    • Google PageRank*
  • Orthogonality
    • Inner Products
    • Orthogonal Sets
    • Orthogonal Projections
    • The Gram-Schmidt Process
    • Least-Squares
  • Symmetric Matrices, Quadratic Forms, and SVD
    • Symmetric Matrices
    • Quadratic Forms
    • Constrained Optimization*
    • Singular Value Decomposition (SVD)*

* Topic not covered in MATH 1553

Class Structure[edit | edit source]

MATH 1554 is a core math class with a focus on theory. However, MATH 1554 does not use formal proofs, and it still does have many computational problems. The theoretical nature of MATH 1554 can be challenging for first-year students who are used to more computation-heavy algebra and calculus courses.

Prerequisite Knowledge[edit | edit source]

Almost no prerequisite knowledge is required, apart from algebra and trigonometry.

Scheduling[edit | edit source]

MATH 1554 is required for math and cs majors. Due to having almost no prerequisites, MATH 1554 is generally taken during freshmen year. Future calculus classes, such as multivariable calculus and differential equations will use linear algebra concepts such as matrices, determinants, and eigenvalues. In addition, linear algebra is especially important for cs majors, who take many classes that require linear algebra, such as MATH 3012 and CS 3510.

Equivalent Courses[edit | edit source]

  • MATH 1553 is the introduction equivalent, which does not cover as many topics as MATH 1554.
  • MATH 1564 is the honors equivalent, which uses proofs and is more theoretical than MATH 1554.

Resources[edit | edit source]

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