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Applied and Computational Mathematics

Spring 2024

This course is a study of linear systems of equations, vector spaces, and linear transformations in the context of applications including basic data fitting, polynomial interpolation and network flow. The following topics and their basic applications are covered: Gaussian elimination, matrix algebra, determinants, eigenvalues and eigenvectors, diagonalization, linear independence, basis and dimension of vector spaces, orthogonality, Gram-Schmidt process and least-squares method. No software is required. Note for those planning to also take EN.625.609 Matrix Theory: EN.625.252 covers a broad range of topics in linear algebra and its applications at an introductory level, while EN.625.609 focuses in depth on the fundamental theoretical properties of matrices and the consequent significant applications. EN.625.252 introduces basic proof writing techniques, theoretical background and knowledge of applications that will be useful for EN.625.609. Prerequisite(s): EN.625.108 Calculus I. Course Note(s): Not for Graduate Credit

The course materials are divided into modules which can be accessed by clicking Modules on the menu. A module will have several sections including the overview, content, readings, and assignments. You are encouraged to preview all sections of the module before starting. Most modules run for a period of seven (7) days, except Module 1, Module 12 and Module 13, see the Course Outline below. You should regularly check the Calendar and Announcements for assignment due dates.

- Linear Systems
- Linear Transformations
- Matrix Algebra
- Determinants
- Vector Spaces
- Eigenvalues and Eigenvectors
- Diagonalization
- Orthogonality and Projections
- Least Squares
- Symmetric Matrices and Quadratic forms

The main goal of the course is to see the beautiful interplay between geometry and basic algebra that allows to solve many fundamental problems in finite-dimensional linear spaces.

- Use algebraic skills essential for the study of systems of linear equations, matrix algebra, vector spaces, eigenvalues and eigenvectors, orthogonality and diagonalization, and least-squares method.
- Use spatial reasoning and geometric properties to solve problems and visualize solutions in two- and three-dimensional settings as well as conceptually extend these results to higher dimensions.
- Critically analyze and construct mathematical arguments that relate to the study of introductory linear algebra.
- Synthesize mathematical statements, ideas, and results by using correct mathematical definitions, terminology, and symbols

Lay, D. C. et al (2020). Linear Algebra and its Applications (6th ed.) Pearson Education. **ISBN-13: 9780135851258**

Textbook information for this course is available online through the appropriate bookstore website: For online courses, search the MBS website.

Strang, G. (1980). Linear Algebra and its Applications (2nd ed.) Academic Press.

It is expected that each module will take approximately 8-11 hours per week to complete. Here is an approximate breakdown: online lectures (3 hours per week), reading the assigned sections of the texts (approximately 2–3 hours per week), and writing assignments (approximately 3–5 hours per week). This course will consist of the following basic student requirements:

Assignments will consist of problem sets. Include your name and a page number indicator (i.e., page x of y) on each page of your submissions. Each problem should have the problem statement, assumptions, computations, and conclusions/discussion delineated. All Figures and Tables should be captioned and labeled appropriately. All assignments are due according to the dates in the Calendar.

Late submissions will not be accepted.

Quantitative assignments are evaluated by the following grading elements:

- Each part of question is answered (20%)
- Assumptions are clearly stated (20%)
- Intermediate derivations and calculations are provided (25%)
- Answer is technically correct and is clearly indicated (25%)
- Answer precision and units are appropriate (10%)

Quantitative assignments are graded as follows:

100–90 = A—All parts of question are addressed; All assumptions are clearly stated; All intermediate derivations and calculations are provided; Answer is technically correct and is clearly indicated; Answer precision and units are appropriate.

89–80 = B—All parts of question are addressed; All assumptions are clearly stated; Some intermediate derivations and calculations are provided; Answer is technically correct and is indicated; Answer precision and units are appropriate.

79–70=C—Most parts of question are addressed; Assumptions are partially stated; Few intermediate derivations and calculations are provided; Answer is not technically correct but is indicated; Answer precision and units are indicated but inappropriate.

<70=F—Some parts of the question are addressed; Assumptions are not stated; Intermediate derivations and calculations are not provided; The answer is incorrect or missing; The answer precision and units are inappropriate or missing.

Each Module will include a timed online quiz. You will have one attempt to complete the quiz. You should attempt the quiz after you have finished all other activities in the module. The quizzes will cover your understanding of the main concepts in each module. They are meant to be challenging.

**Exams (50% of Final Grade Calculation, combined from 15% for each exam and 20% for Final)**

The first exam will be available in Module 5, the second - in Module 10, the final exam - in Module 14. Each exam is a two-hour exam that will use a LockDown browser. The exams are closed book, no calculator. The exams are evaluated by the following grading elements:

- Each part of question is answered (20%)
- Assumptions are clearly stated (20%)
- Intermediate derivations and calculations are provided (25%)
- Answer is technically correct and is clearly indicated (25%)
- Answer precision and units are appropriate (10%)

Exams are graded as follows:

100–90 = A—All parts of question are addressed; All assumptions are clearly stated; All intermediate derivations and calculations are provided; Answer is technically correct and is clearly indicated; Answer precision and units are appropriate.

89–80 = B—All parts of question are addressed; All assumptions are clearly stated; Some intermediate derivations and calculations are provided; Answer is technically correct and is indicated. Answer precision and units are indicated..

79–70=C—Most parts of question are addressed; Assumptions are partially stated; Few intermediate derivations and calculations are provided; Answer is not technically correct but is indicated; Answer precision and units are indicated but inappropriate.

<70=F—Some parts of the question are addressed; Assumptions are not stated; Intermediate derivations and calculations are not provided; The answer is incorrect or missing; The answer precision and units are inappropriate or missing.

Free software to help you master linear algebra. The link is on the menu in Canvas. You must join your classroom to participate. The setup is similar to Duolingo, i.e., a task is not marked complete until you have mastered it. In our classroom there are 79 tasks. If you complete all 79 tasks, I will add 4% to your final grade. If you complete at least 75 tasks, I will add 3% to your final grade. If you complete at least 70 tasks, I will add 2% to your final grade. If you complete at least 65 tasks, I will add 1% to your final grade.

EP uses a +/- grading system (see “Grading System”, *Graduate Programs *catalog, p. 10).

Score Range | Letter Grade |
---|---|

100-98 | = A+ |

97-94 | = A |

93-90 | = A− |

89-87 | = B+ |

86-83 | = B |

82-80 | = B− |

79-77 | = C+ |

76-73 | = C |

72-70 | = C− |

69-67 | = D+ |

66-63 | = D |

<63 | = F |

Final grades will be determined by the following weighting:

Item | % of Grade |

Assignments | 45% |

Quizzes | 5% |

Exam 1 | 15% |

Exam 2 | 15% |

Final Exam | 20% |

Total | 100% |

**Deadlines for Adding, Dropping and Withdrawing from Courses **

Students may add a course up to one week after the start of the term for that particular course. Students may drop courses according to the drop deadlines outlined in the EP academic calendar (https://ep.jhu.edu/student-services/academic-calendar/). Between the 6th week of the class and prior to the final withdrawal deadline, a student may withdraw from a course with a W on their academic record. A record of the course will remain on the academic record with a W appearing in the grade column to indicate that the student registered and withdrew from the course.

**Academic Misconduct Policy**

All students are required to read, know, and comply with the Johns Hopkins University Krieger School of Arts and Sciences (KSAS) / Whiting School of Engineering (WSE) Procedures for Handling Allegations of Misconduct by Full-Time and Part-Time Graduate Students.

This policy prohibits academic misconduct, including but not limited to the following: cheating or facilitating cheating; plagiarism; reuse of assignments; unauthorized collaboration; alteration of graded assignments; and unfair competition. Course materials (old assignments, texts, or examinations, etc.) should not be shared unless authorized by the course instructor. Any questions related to this policy should be directed to EP’s academic integrity officer at ep-academic-integrity@jhu.edu.

**Students with Disabilities - Accommodations and Accessibility**

Johns Hopkins University values diversity and inclusion. We are committed to providing welcoming, equitable, and accessible educational experiences for all students. Students with disabilities (including those with psychological conditions, medical conditions and temporary disabilities) can request accommodations for this course by providing an Accommodation Letter issued by Student Disability Services (SDS). Please request accommodations for this course as early as possible to provide time for effective communication and arrangements.

For further information or to start the process of requesting accommodations, please contact Student Disability Services at Engineering for Professionals, ep-disability-svcs@jhu.edu.

**Student Conduct Code**

The fundamental purpose of the JHU regulation of student conduct is to promote and to protect the health, safety, welfare, property, and rights of all members of the University community as well as to promote the orderly operation of the University and to safeguard its property and facilities. As members of the University community, students accept certain responsibilities which support the educational mission and create an environment in which all students are afforded the same opportunity to succeed academically.

For a full description of the code please visit the following website: https://studentaffairs.jhu.edu/policies-guidelines/student-code/

**Classroom Climate**

JHU is committed to creating a classroom environment that values the diversity of experiences and perspectives that all students bring. Everyone has the right to be treated with dignity and respect. Fostering an inclusive climate is important. Research and experience show that students who interact with peers who are different from themselves learn new things and experience tangible educational outcomes. At no time in this learning process should someone be singled out or treated unequally on the basis of any seen or unseen part of their identity.

If you have concerns in this course about harassment, discrimination, or any unequal treatment, or if you seek accommodations or resources, please reach out to the course instructor directly. Reporting will never impact your course grade. You may also share concerns with your program chair, the Assistant Dean for Diversity and Inclusion, or the Office of Institutional Equity. In handling reports, people will protect your privacy as much as possible, but faculty and staff are required to officially report information for some cases (e.g. sexual harassment).

**Course Auditing**

When a student enrolls in an EP course with “audit” status, the student must reach an understanding with the instructor as to what is required to earn the “audit.” If the student does not meet those expectations, the instructor must notify the EP Registration Team [EP-Registration@exchange.johnshopkins.edu] in order for the student to be retroactively dropped or withdrawn from the course (depending on when the "audit" was requested and in accordance with EP registration deadlines). All lecture content will remain accessible to auditing students, but access to all other course material is left to the discretion of the instructor.