Linear Algebra Course

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Linear Algebra Course

•  
• Activity 2 Finding Similarities and
  Dissimilarities in DNA Sequences of HIV Patients
• Objective
• Classify the types of Distances Matrices
  resulting from the alignment of DNA sequences of
  certain viruses and investigate the properties of
  symmetric Matrices.
• Learning Goals
• Mathematics Majors can appreciate the beauty of
  mathematics and its application for solving real
  world problems arising from Biological data.
• Mathematical Keywords
• Symmetric Matrix
• Eigenvalues
• Biological Keywords
• HIV
• DNA sequence
• CD4 Counts (counting
  t-helper lymphocytes)
• DNA Distance Matrices
• Un rooted Trees
• Methodology
• Present the students a Case Study related to HIV
  virus. Ask the students to formulate questions
  about what they know and what they need to know
  about the case in order to find similarities and
  dissimilarities in the DNA sequences of the virus
  in diagnosed HIV subjects. Provide the students
  a table with the summarized data of the HIV Study
  using DNA sequences and let them analyze the data
  using a particular software that can be obtained
  free on the web. Show the student how to obtain
  the DNA sequences of the virus using this
  software and ask them to find the DNA Distance
  Matrices using the same tool. This can be done
  in small groups assigning two or three subjects
  to each group and then collecting the information
  for all the subjects. Once the Distance Matrices
  are gathered, explain the concept of symmetric
  matrices and their properties. Define and compute
  the eigenvalues of the symmetric matrices and ask
  the students, that applying this concepts to the
  DNA distances matrices that they already have
  analyzed the data an draw conclusions about the
  similarities or dissimilarities of the DNA
  sequences of the HIV-1 virus found on infected
  subjects.
• Technological Tools
• Biology Workbench

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DNA DISTANCE Matrix for Subject 3 Visit 5
10 (1) (2) (3) (4)
(5) (6) (7) (8) (9) (10)
(1) S3V5-10 0.0000 0.0070 0.0214 0.0214
0.0106 0.0214 0.0177 0.0177 0.0141 0.0286
(2) S3V5-7 0.0070 0.0000 0.0214 0.0142
0.0106 0.0214 0.0106 0.0106 0.0070 0.0214
(3) S3V5-5 0.0214 0.0214 0.0000 0.0071
0.0106 0.0214 0.0106 0.0251 0.0214 0.0324
(4) S3V5-4 0.0214 0.0142 0.0071 0.0000
0.0106 0.0142 0.0107 0.0178 0.0142 0.0251
(5) S3V5-8 0.0106 0.0106 0.0106 0.0106
0.0000 0.0177 0.0142 0.0214 0.0177 0.0286
(6) S3V5-2 0.0214 0.0214 0.0214 0.0142
0.0177 0.0000 0.0178 0.0250 0.0214 0.0323
(7) S3V5-6 0.0177 0.0106 0.0106 0.0107
0.0142 0.0178 0.0000 0.0142 0.0106 0.0214
(8) S3V5-9 0.0177 0.0106 0.0251 0.0178
0.0214 0.0250 0.0142 0.0000 0.0106 0.0250
(9) S3V5-1 0.0141 0.0070 0.0214 0.0142
0.0177 0.0214 0.0106 0.0106 0.0000 0.0142
(10) S3V5-3 0.0286 0.0214 0.0324 0.0251
0.0286 0.0323 0.0214 0.0250 0.0142 0.0000
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