2. Linear Algebra for Machine Learning: Basis and DimensionCeni Babaoglu, PhD
The seminar series will focus on the mathematical background needed for machine learning. The first set of the seminars will be on "Linear Algebra for Machine Learning". Here are the slides of the second part which is discussing basis and dimension.
Here is the link of the first part which was discussing linear systems: https://www.slideshare.net/CeniBabaogluPhDinMat/linear-algebra-for-machine-learning-linear-systems/1
1. Linear Algebra for Machine Learning: Linear SystemsCeni Babaoglu, PhD
The seminar series will focus on the mathematical background needed for machine learning. The first set of the seminars will be on "Linear Algebra for Machine Learning". Here are the slides of the first part which is giving a short overview of matrices and discussing linear systems.
4. Linear Algebra for Machine Learning: Eigenvalues, Eigenvectors and Diagona...Ceni Babaoglu, PhD
The seminar series will focus on the mathematical background needed for machine learning. The first set of the seminars will be on "Linear Algebra for Machine Learning". Here are the slides of the fourth part which is discussing eigenvalues, eigenvectors and diagonalization.
Here is the link of the first part which was discussing linear systems: https://www.slideshare.net/CeniBabaogluPhDinMat/linear-algebra-for-machine-learning-linear-systems/1
Here are the slides of the second part which was discussing basis and dimension:
https://www.slideshare.net/CeniBabaogluPhDinMat/2-linear-algebra-for-machine-learning-basis-and-dimension
Here are the slides of the third part which is discussing factorization and linear transformations.
https://www.slideshare.net/CeniBabaogluPhDinMat/3-linear-algebra-for-machine-learning-factorization-and-linear-transformations-130813437
2. Linear Algebra for Machine Learning: Basis and DimensionCeni Babaoglu, PhD
The seminar series will focus on the mathematical background needed for machine learning. The first set of the seminars will be on "Linear Algebra for Machine Learning". Here are the slides of the second part which is discussing basis and dimension.
Here is the link of the first part which was discussing linear systems: https://www.slideshare.net/CeniBabaogluPhDinMat/linear-algebra-for-machine-learning-linear-systems/1
1. Linear Algebra for Machine Learning: Linear SystemsCeni Babaoglu, PhD
The seminar series will focus on the mathematical background needed for machine learning. The first set of the seminars will be on "Linear Algebra for Machine Learning". Here are the slides of the first part which is giving a short overview of matrices and discussing linear systems.
4. Linear Algebra for Machine Learning: Eigenvalues, Eigenvectors and Diagona...Ceni Babaoglu, PhD
The seminar series will focus on the mathematical background needed for machine learning. The first set of the seminars will be on "Linear Algebra for Machine Learning". Here are the slides of the fourth part which is discussing eigenvalues, eigenvectors and diagonalization.
Here is the link of the first part which was discussing linear systems: https://www.slideshare.net/CeniBabaogluPhDinMat/linear-algebra-for-machine-learning-linear-systems/1
Here are the slides of the second part which was discussing basis and dimension:
https://www.slideshare.net/CeniBabaogluPhDinMat/2-linear-algebra-for-machine-learning-basis-and-dimension
Here are the slides of the third part which is discussing factorization and linear transformations.
https://www.slideshare.net/CeniBabaogluPhDinMat/3-linear-algebra-for-machine-learning-factorization-and-linear-transformations-130813437
is used. Mathematics is applied in day to day life, so we can now review the concepts of Algebra and its uses in daily life. Here in our work we have made a small split up of items in a bag while shopping. Basic Algebra is where we finally put the algebra in pre-algebra. The concepts taught here will be used in every math class you take from here on. Well introduce you to some exciting stuff like drawing graphs and solving complicated equations. Since we are learning Algebra, Geometry in the school days. But the is a real life application of Algebra which is used in Geometry. Now a days the social media has improved a lot. We cant able to solve those figured puzzles, hence we can solve them by using algebraic equations. S. Ambika | R. Mythrae | S. Saranya | K. Selvanayaki "Algebra in Real Life" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-3 | Issue-2 , February 2019, URL: https://www.ijtsrd.com/papers/ijtsrd21517.pdf
Paper URL: https://www.ijtsrd.com/mathemetics/algebra/21517/algebra-in-real-life/s-ambika
A review of the growth of the Israel Genealogy Research Association Database Collection for the last 12 months. Our collection is now passed the 3 million mark and still growing. See which archives have contributed the most. See the different types of records we have, and which years have had records added. You can also see what we have for the future.
This presentation includes basic of PCOS their pathology and treatment and also Ayurveda correlation of PCOS and Ayurvedic line of treatment mentioned in classics.
Unit 8 - Information and Communication Technology (Paper I).pdfThiyagu K
This slides describes the basic concepts of ICT, basics of Email, Emerging Technology and Digital Initiatives in Education. This presentations aligns with the UGC Paper I syllabus.
Biological screening of herbal drugs: Introduction and Need for
Phyto-Pharmacological Screening, New Strategies for evaluating
Natural Products, In vitro evaluation techniques for Antioxidants, Antimicrobial and Anticancer drugs. In vivo evaluation techniques
for Anti-inflammatory, Antiulcer, Anticancer, Wound healing, Antidiabetic, Hepatoprotective, Cardio protective, Diuretics and
Antifertility, Toxicity studies as per OECD guidelines
June 3, 2024 Anti-Semitism Letter Sent to MIT President Kornbluth and MIT Cor...Levi Shapiro
Letter from the Congress of the United States regarding Anti-Semitism sent June 3rd to MIT President Sally Kornbluth, MIT Corp Chair, Mark Gorenberg
Dear Dr. Kornbluth and Mr. Gorenberg,
The US House of Representatives is deeply concerned by ongoing and pervasive acts of antisemitic
harassment and intimidation at the Massachusetts Institute of Technology (MIT). Failing to act decisively to ensure a safe learning environment for all students would be a grave dereliction of your responsibilities as President of MIT and Chair of the MIT Corporation.
This Congress will not stand idly by and allow an environment hostile to Jewish students to persist. The House believes that your institution is in violation of Title VI of the Civil Rights Act, and the inability or
unwillingness to rectify this violation through action requires accountability.
Postsecondary education is a unique opportunity for students to learn and have their ideas and beliefs challenged. However, universities receiving hundreds of millions of federal funds annually have denied
students that opportunity and have been hijacked to become venues for the promotion of terrorism, antisemitic harassment and intimidation, unlawful encampments, and in some cases, assaults and riots.
The House of Representatives will not countenance the use of federal funds to indoctrinate students into hateful, antisemitic, anti-American supporters of terrorism. Investigations into campus antisemitism by the Committee on Education and the Workforce and the Committee on Ways and Means have been expanded into a Congress-wide probe across all relevant jurisdictions to address this national crisis. The undersigned Committees will conduct oversight into the use of federal funds at MIT and its learning environment under authorities granted to each Committee.
• The Committee on Education and the Workforce has been investigating your institution since December 7, 2023. The Committee has broad jurisdiction over postsecondary education, including its compliance with Title VI of the Civil Rights Act, campus safety concerns over disruptions to the learning environment, and the awarding of federal student aid under the Higher Education Act.
• The Committee on Oversight and Accountability is investigating the sources of funding and other support flowing to groups espousing pro-Hamas propaganda and engaged in antisemitic harassment and intimidation of students. The Committee on Oversight and Accountability is the principal oversight committee of the US House of Representatives and has broad authority to investigate “any matter” at “any time” under House Rule X.
• The Committee on Ways and Means has been investigating several universities since November 15, 2023, when the Committee held a hearing entitled From Ivory Towers to Dark Corners: Investigating the Nexus Between Antisemitism, Tax-Exempt Universities, and Terror Financing. The Committee followed the hearing with letters to those institutions on January 10, 202
2024.06.01 Introducing a competency framework for languag learning materials ...Sandy Millin
http://sandymillin.wordpress.com/iateflwebinar2024
Published classroom materials form the basis of syllabuses, drive teacher professional development, and have a potentially huge influence on learners, teachers and education systems. All teachers also create their own materials, whether a few sentences on a blackboard, a highly-structured fully-realised online course, or anything in between. Despite this, the knowledge and skills needed to create effective language learning materials are rarely part of teacher training, and are mostly learnt by trial and error.
Knowledge and skills frameworks, generally called competency frameworks, for ELT teachers, trainers and managers have existed for a few years now. However, until I created one for my MA dissertation, there wasn’t one drawing together what we need to know and do to be able to effectively produce language learning materials.
This webinar will introduce you to my framework, highlighting the key competencies I identified from my research. It will also show how anybody involved in language teaching (any language, not just English!), teacher training, managing schools or developing language learning materials can benefit from using the framework.
Read| The latest issue of The Challenger is here! We are thrilled to announce that our school paper has qualified for the NATIONAL SCHOOLS PRESS CONFERENCE (NSPC) 2024. Thank you for your unwavering support and trust. Dive into the stories that made us stand out!
Acetabularia Information For Class 9 .docxvaibhavrinwa19
Acetabularia acetabulum is a single-celled green alga that in its vegetative state is morphologically differentiated into a basal rhizoid and an axially elongated stalk, which bears whorls of branching hairs. The single diploid nucleus resides in the rhizoid.
Executive Directors Chat Leveraging AI for Diversity, Equity, and InclusionTechSoup
Let’s explore the intersection of technology and equity in the final session of our DEI series. Discover how AI tools, like ChatGPT, can be used to support and enhance your nonprofit's DEI initiatives. Participants will gain insights into practical AI applications and get tips for leveraging technology to advance their DEI goals.
Executive Directors Chat Leveraging AI for Diversity, Equity, and Inclusion
Math 1300: Section 5-1 Inequalities in Two Variables
1. Graphing Linear Inequalities in Two Variables
Application
Math 1300 Finite Mathematics
Section 5.1 Inequalities in Two Variables
Jason Aubrey
Department of Mathematics
University of Missouri
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Jason Aubrey Math 1300 Finite Mathematics
2. Graphing Linear Inequalities in Two Variables
Application
We know how to graph linear equations such as
y = 2x − 3 and 2x − 3y = 5
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Jason Aubrey Math 1300 Finite Mathematics
3. Graphing Linear Inequalities in Two Variables
Application
We know how to graph linear equations such as
y = 2x − 3 and 2x − 3y = 5
But how do we graph linear inequalities such as the following?
y ≤ 2x − 3 and 2x − 3y > 5
university-logo
Jason Aubrey Math 1300 Finite Mathematics
4. Graphing Linear Inequalities in Two Variables
Application
We know how to graph linear equations such as
y = 2x − 3 and 2x − 3y = 5
But how do we graph linear inequalities such as the following?
y ≤ 2x − 3 and 2x − 3y > 5
Before we introduce the procedure for this, we discuss some
relevant terminology.
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Jason Aubrey Math 1300 Finite Mathematics
5. Graphing Linear Inequalities in Two Variables
Application
A vertical line divides the plane into left and right half-planes.
A non-vertical line divides it into upper and lower half-planes.
The dividing line is called the boundary line of each half-plane.
Boundary Line → Boundary Line→
Upper
half-plane
Left Right Lower
half-plane half-plane half-plane
x x
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Jason Aubrey Math 1300 Finite Mathematics
6. Graphing Linear Inequalities in Two Variables
Application
The graph of the linear inequality
Ax + By < C or Ax + By > C
with B = 0, is either the upper half-plane or the lower half-plane
(but not both) determined by the line Ax + By = C.
university-logo
Jason Aubrey Math 1300 Finite Mathematics
7. Graphing Linear Inequalities in Two Variables
Application
The graph of the linear inequality
Ax + By < C or Ax + By > C
with B = 0, is either the upper half-plane or the lower half-plane
(but not both) determined by the line Ax + By = C.
If B = 0 and A = 0, the graph of
Ax < C or Ax > C
is either the left half-plane or the right half-plane (but not both)
determined by the line Ax = C.
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Jason Aubrey Math 1300 Finite Mathematics
8. Graphing Linear Inequalities in Two Variables
Application
Procedure for Graphing Linear Inequalities
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Jason Aubrey Math 1300 Finite Mathematics
9. Graphing Linear Inequalities in Two Variables
Application
Procedure for Graphing Linear Inequalities
Step 1. First graph Ax + By = C as a dashed line if equality is
not included in the original statement or as a solid line if
equality is included.
university-logo
Jason Aubrey Math 1300 Finite Mathematics
10. Graphing Linear Inequalities in Two Variables
Application
Procedure for Graphing Linear Inequalities
Step 1. First graph Ax + By = C as a dashed line if equality is
not included in the original statement or as a solid line if
equality is included.
Step 2. Choose a test point anywhere in the plane not on the
line [the origin usually requires the least computation] and
substitute the coordinates into the inequality.
university-logo
Jason Aubrey Math 1300 Finite Mathematics
11. Graphing Linear Inequalities in Two Variables
Application
Procedure for Graphing Linear Inequalities
Step 1. First graph Ax + By = C as a dashed line if equality is
not included in the original statement or as a solid line if
equality is included.
Step 2. Choose a test point anywhere in the plane not on the
line [the origin usually requires the least computation] and
substitute the coordinates into the inequality.
Step 3. The graph of the original inequality includes the
half-plane containing the test point if the inequality is satisfied
by that point or the half-plane not containing the test-point if the
inequality is not satisfied by that point. Clearly indicate which
half-plane is included in the graph by writing "Feasible Set" or
"FS" in that half-plane.
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Jason Aubrey Math 1300 Finite Mathematics
12. Graphing Linear Inequalities in Two Variables
Application
Example: Graph the inequality y ≤ x − 1.
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Jason Aubrey Math 1300 Finite Mathematics
13. Graphing Linear Inequalities in Two Variables
Application
Example: Graph the inequality y ≤ x − 1.
Step 1. Graph the boundary line.
2
x y
0 -1
1
1 0
−2 −1 0 1 2
−1
y =x −1
−2
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Jason Aubrey Math 1300 Finite Mathematics
14. Graphing Linear Inequalities in Two Variables
Application
Example: Graph the inequality y ≤ x − 1.
Step 1. Graph the boundary line.
2
x y
0 -1
1
1 0
(0, 0) Step 2. Test (upper) half plane with
−2 −1 0 1 2 (0, 0).
−1 0 ≤ 0−1 No!
y =x −1 ?
−2
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Jason Aubrey Math 1300 Finite Mathematics
15. Graphing Linear Inequalities in Two Variables
Application
Example: Graph the inequality y ≤ x − 1.
Step 1. Graph the boundary line.
2
x y
0 -1
1
1 0
(0, 0) Step 2. Test (upper) half plane with
−2 −1 0 1 2 (0, 0).
−1 Feasible 0 ≤ 0−1 No!
y =x −1 Set ?
−2
Step 3. Indicate feasible set.
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Jason Aubrey Math 1300 Finite Mathematics
16. Graphing Linear Inequalities in Two Variables
Application
Example: Graph the inequality 6x + 4y ≥ 24
6
5
4
3
2
1
0 1 2 3 4
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Jason Aubrey Math 1300 Finite Mathematics
17. Graphing Linear Inequalities in Two Variables
Application
Example: Graph the inequality 6x + 4y ≥ 24
Step 1. Graph the boundary line.
6 x y
5 0 6
4 4 0
3
2
1
0 1 2 3 4
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Jason Aubrey Math 1300 Finite Mathematics
18. Graphing Linear Inequalities in Two Variables
Application
Example: Graph the inequality 6x + 4y ≥ 24
Step 1. Graph the boundary line.
6 x y
5 0 6
4 4 0
3 Step 2. Test (lower) half plane with
2 (0, 0).
1 (0, 0) 6(0) + 4(0) ≥ 24 No!
0 1 2 3 4 ?
university-logo
Jason Aubrey Math 1300 Finite Mathematics
19. Graphing Linear Inequalities in Two Variables
Application
Example: Graph the inequality 6x + 4y ≥ 24
Step 1. Graph the boundary line.
6 x y
5
FS 0 6
4 4 0
3 Step 2. Test (lower) half plane with
2 (0, 0).
1 (0, 0) 6(0) + 4(0) ≥ 24 No!
0 1 2 3 4 ?
Step 3. Indicate feasible set.
university-logo
Jason Aubrey Math 1300 Finite Mathematics
20. Graphing Linear Inequalities in Two Variables
Application
Example: Graph the inequality 25x + 40y ≤ 3000, subject to
the non-negative restrictions x ≥ 0, y ≥ 0.
70
60
50
40
30
20
10
20 40 60 80 100 120
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Jason Aubrey Math 1300 Finite Mathematics
21. Graphing Linear Inequalities in Two Variables
Application
Example: Graph the inequality 25x + 40y ≤ 3000, subject to
the non-negative restrictions x ≥ 0, y ≥ 0.
Step 1. Graph the boundary line.
70 x y
60 0 75
50 120 0
40
30
20
10
20 40 60 80 100 120
university-logo
Jason Aubrey Math 1300 Finite Mathematics
22. Graphing Linear Inequalities in Two Variables
Application
Example: Graph the inequality 25x + 40y ≤ 3000, subject to
the non-negative restrictions x ≥ 0, y ≥ 0.
Step 1. Graph the boundary line.
70 x y
60 0 75
50 120 0
40
Step 2. Test (lower) half plane with
30
(0, 0).
20
10 25(0) + 40(0) ≤ 3000 Yes!
(0, 0)
?
20 40 60 80 100 120
university-logo
Jason Aubrey Math 1300 Finite Mathematics
23. Graphing Linear Inequalities in Two Variables
Application
Example: Graph the inequality 25x + 40y ≤ 3000, subject to
the non-negative restrictions x ≥ 0, y ≥ 0.
Step 1. Graph the boundary line.
70 x y
60 0 75
50 120 0
40
Step 2. Test (lower) half plane with
30
FS (0, 0).
20
10 25(0) + 40(0) ≤ 3000 Yes!
(0, 0)
?
20 40 60 80 100 120
Step 3. Indicate feasible set.
university-logo
Jason Aubrey Math 1300 Finite Mathematics
24. Graphing Linear Inequalities in Two Variables
Application
Example: A company produces foam mattresses in two sizes:
regular and king size. It takes 5 minutes to cut the foam for a
regular mattress and 6 minutes for a king size mattress. If the
cutting department has 50 labor-hours available each day, how
many regular and king size mattresses can be cut in one day?
Express your answer as a linear inequality with appropriate
nonnegative restrictions and draw its graph.
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Jason Aubrey Math 1300 Finite Mathematics
25. Graphing Linear Inequalities in Two Variables
Application
x = number of regular mattresses
y = number of king size matresses
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Jason Aubrey Math 1300 Finite Mathematics
26. Graphing Linear Inequalities in Two Variables
Application
x = number of regular mattresses
y = number of king size matresses
5x + 6y ≤ 3000
x ≥0 y ≥0
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Jason Aubrey Math 1300 Finite Mathematics
27. Graphing Linear Inequalities in Two Variables
Application
500
400
300
200
100
−100 0 100 200 300 400 500 600
−100
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Jason Aubrey Math 1300 Finite Mathematics
28. Graphing Linear Inequalities in Two Variables
Application
Step 1. Graph the boundary
line.
500 x y
0 500
400 600 0
300
200
100
−100 0 100 200 300 400 500 600
−100
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Jason Aubrey Math 1300 Finite Mathematics
29. Graphing Linear Inequalities in Two Variables
Application
Step 2. Test (lower) half plane
with (0, 0).
500
5(0) + 6(0) ≤ 3000 Yes!
?
400
300
200
100
(0, 0)
−100 0 100 200 300 400 500 600
−100
university-logo
Jason Aubrey Math 1300 Finite Mathematics
30. Graphing Linear Inequalities in Two Variables
Application
Step 2. Test (lower) half plane
with (0, 0).
500
5(0) + 6(0) ≤ 3000 Yes!
?
400
Step 3. Indicate feasible set.
300
200 FS
100
(0, 0)
−100 0 100 200 300 400 500 600
−100
university-logo
Jason Aubrey Math 1300 Finite Mathematics