Difference between revisions of "MATH 1554"

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{{DISPLAYTITLE:MATH 1554 - Linear Algebra}}
  
{{DISPLAYTITLE:MATH 1554 - Linear Algebra}}
   
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'''MATH 1554''' is a 4 credit core [[Mathematics|math]] class in linear algebra.
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==Class Structure ==
  
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===Workload===
  
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Content in MATH 1554 is typically assessed through homework, quizzes, and exams. These tend to have a mix of questions on theory, often given as true/false questions, and computation. While the course requires no formal proofs, the theoretical nature of MATH 1554 can be challenging for first-year students. Homework may not be very time-consuming, but questions often involve a bit of thinking.
  
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===Topic List===
  
−
#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
  
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##Inner Products
  
−
##Orthogonal Sets
  
−
##Orthogonal Projections
  
−
##The Gram-Schmidt Process
  
−
##Least-Squares
  
−
#Symmetric Matrices and Quadratic Forms
  
−
##Symmetric Matrices
  
−
##Quadratic Forms
  
−
##Constrained Optimization*
  
−
##Singular Value Decomposition (SVD)*
  
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<nowiki>*</nowiki> Topic not covered in MATH 1553
  
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=== Prerequisite Knowledge===
  
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Almost no prerequisite knowledge is required, apart from algebra and trigonometry.
  
−
===Relation to the Overall Curriculum===
  
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MATH 1554 is generally taken by freshmen due to it having almost no prerequisites. However, future calculus classes, such as [[MATH 2550]], [[MATH 2551]], and [[MATH 2552]] will use linear algebra concepts such as matrices, determinants, and eigenvalues. In addition, linear algebra is important for [[Computer Science|computer science]] majors, who have to take classes like [[MATH 3012]] and [[CS 3510]], which require linear algebra.
  
−
===Resources===
  
   
  +
==Topic List ==
−
* https://gatech.instructure.com/courses/114544 provides a set of videos and old exams for MATH 1554.
  
  +
*Linear Systems and Transformations
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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.
  
  +
** Systems of Linear Equations
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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.
  
  +
** Row Reduction and Echelon Forms
  +
** Vector Equations
  +
** The Matrix Equation
  +
** Solution Sets of Linear Systems
  +
** Linear Independence
  +
** Linear Transforms
   
  +
*Matrices and the Matrix Inverse
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== Current Registration Info ==
  
  +
** Matrix Operations
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{{LinkedStudio}}
  
  +
** Matrix Inverse
  +
** Invertible Matrix Theorem
  +
** Partitioned Matrices*
  +
** LU Factorization
  +
** Leontief Input-Output Model*
  +
** Computer Graphics*
  +
** Subspaces
  +
** Dimension and Rank
   
  +
*Determinants and Eigenvalues
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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]
  
  +
** Determinants
  +
** Volume and Linear Transforms*
  +
** Markov Chains*
  +
** Eigenvalues and Eigenvectors
  +
** Characteristic Equation
  +
** Diagonalization
  +
** Complex Eigenvalues*
  +
** Google PageRank*
   
  +
*Orthogonality
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=== Prerequisites ===
  
  +
** Inner Products
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At least one of the following<ref>https://oscar.gatech.edu/bprod/bwckctlg.p_disp_course_detail?cat_term_in=202108&subj_code_in=MATH&crse_numb_in=1554</ref><ref>https://math.gatech.edu/courses/math/1554</ref>:
  
  +
** Orthogonal Sets
  +
** Orthogonal Projections
  +
** The Gram-Schmidt Process
  +
** Least-Squares
   
  +
*Symmetric Matrices, Quadratic Forms, and SVD
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* D or higher in MATH 1113 (Precalculus).
  
  +
** Symmetric Matrices
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* D or higher in MATH 1552 (Integral Calculus) or equivalent.
  
  +
** Quadratic Forms
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* 620 or higher on the Math section of the SAT
  
  +
** Constrained Optimization*
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* 26 or higher on the Math section of the ACT.
  
  +
** Singular Value Decomposition (SVD)*
  +
<nowiki>*</nowiki> Topic not covered in [[MATH 1553]]
   
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=== Equivalent Courses ===
 +
== Workload ==
  +
Content in MATH 1554 is typically assessed through homework, quizzes, and exams. These tend to have a mix of questions on theory, often given as true/false questions, and computation. While the course requires no formal proofs, the theoretical nature of MATH 1554 can be challenging for first-year students. Homework may not be very time-consuming, but questions often involve a bit of thinking.
  +
== Prerequisite Knowledge==
  +
Almost no prerequisite knowledge is required, apart from algebra and trigonometry.
  +
== Equivalent Courses ==
 
[[MATH 1564]]. If you enjoy theoretical math and proofs a lot, and consider yourself very good at math, consider taking MATH 1564 instead.
  
[[MATH 1564]]. If you enjoy theoretical math and proofs a lot, and consider yourself very good at math, consider taking MATH 1564 instead.
  +
*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.
  +
==Future Outlook==
  +
MATH 1554 is generally taken by freshmen due to it having almost no prerequisites. However, future calculus classes, such as [[MATH 2550]], [[MATH 2551]], and [[MATH 2552]] will use linear algebra concepts such as matrices, determinants, and eigenvalues. In addition, linear algebra is important for [[Computer Science|computer science]] majors, who have to take classes that require linear algebra, such as [[MATH 3012]] and [[CS 3510]].
  +
== Registration ==
  +
MATH 1554 is a [[Linked Course|linked course]] with a studio.
   
  +
== Resources ==
−
=== Majors That Require This Class ===
  
  +
* https://gatech.instructure.com/courses/114544 provides a set of videos and old exams for MATH 1554.
−  
  +
*[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.
−
* Applied Physics
  
  +
*[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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* 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
  
 
[[Category:Courses|^MATH^MATH]]
  
[[Category:Courses|^MATH^MATH]]

Revision as of 17:18, 1 July 2021


MATH 1554 is a 4 credit core math class in linear algebra.

Topic List

  • 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

Workload

Content in MATH 1554 is typically assessed through homework, quizzes, and exams. These tend to have a mix of questions on theory, often given as true/false questions, and computation. While the course requires no formal proofs, the theoretical nature of MATH 1554 can be challenging for first-year students. Homework may not be very time-consuming, but questions often involve a bit of thinking.

Prerequisite Knowledge

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

Equivalent Courses

MATH 1564. If you enjoy theoretical math and proofs a lot, and consider yourself very good at math, consider taking MATH 1564 instead.

  • 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.

Future Outlook

MATH 1554 is generally taken by freshmen due to it having almost no prerequisites. However, future calculus classes, such as MATH 2550, MATH 2551, and MATH 2552 will use linear algebra concepts such as matrices, determinants, and eigenvalues. In addition, linear algebra is important for computer science majors, who have to take classes that require linear algebra, such as MATH 3012 and CS 3510.

Registration

MATH 1554 is a linked course with a studio.

Resources

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