lectures/general_info.ipynb

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    "# Numerical linear algebra, Skoltech,  Fall 2022,  general course info"
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    "## About the course\n",
    "\n",
    "- The course is about solving problems arising in computing\n",
    "- Three main problems:\n",
    "    - solving linear systems\n",
    "    - finding eigenvalues and eigenvectors\n",
    "    - computing matrix functions (matrix exponential especially)\n",
    "- The methods are different for small-scale and large-scale problems:\n",
    "    - using matrix decompositions\n",
    "    - iterative methods"
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    "## Learning outcomes\n",
    "\n",
    "-  Solve medium-scale numerical linear algebra problems \n",
    "(solve linear systems, compute eigenvalues and eigenvectors, solve linear least squares) using **matrix factorizations**\n",
    "-  **Iterative methods** for sparse/structured systems\n",
    "- Find which methods are the most appropriate for the particular problem\n",
    "-  Find appropriate software"
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    "## (Approximate) Syllabus\n",
    "\n",
    "- **Week 1:** Intro and floating points arithmetics, matrices, vectors, norms, ranks. \n",
    "- **Week 2:** Matrix decompositions 1: SVD and its applications\n",
    "- **Week 3:** Matrix decompositions 2: Linear systems and LU, eigendecomposition\n",
    "- **Week 4:** Matrix decompositions 3: QR and Schur + project proposal deadline\n",
    "- **Week 5:** Sparse and structured matrices, iterative methods (part 1)\n",
    "- **Week 6:** Iterative methods (part 2), matrix functions and advanced topics\n",
    "- **Week 7:** Oral exam (two days)\n",
    "- **Week 8:** Application period and project presentations"
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    "## Lecture access\n",
    "\n",
    "- Lectures can be downloaded and viewed on GitHub: https://github.com/oseledets/nla2022\n",
    "\n",
    "- They can also be viewed online using nbviewer: http://nbviewer.jupyter.org/github/oseledets/nla2022/tree/master/"
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    "## Team\n",
    "Course instructor: Ivan Oseledets\n",
    "\n",
    "TAs: Alexander Katrutsa, Gleb Mezentsev, \n",
    "Anna Rudenko, Egor Sevriugov, Daria Cherniuk, Daniil Merkulov, Mikhail Pautov"
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    "## How do we grade\n",
    "- **50%** homework. Includes 3 problem sets with coding in Python and theoretical problems.\n",
    "- **20%** final exam - the format and rules will be announced later\n",
    "- **15%** Midterm test -- written test with simple problems.\n",
    "- **15%** term project. More details and policies about this activity will be presented later.\n",
    "- **10%** Bonus. Solve bonus tasks from HW.\n",
    "\n",
    "Total maximum is **110%**."
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    "## Problem sets\n",
    "\n",
    "1. Homework is distributed in **Jupyter notebooks**\n",
    "\n",
    "2. Problem sets contain both **theoretical** and **programming** tasks\n",
    "\n",
    "3. No hand-written solutions are accepted, only Markdown and $\\LaTeX$ text in the single Jupyter Notebook file is Ok."
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    "## Problem set rules\n",
    "\n",
    "1. Solutions must be submitted on **Canvas** before the deadline\n",
    "3. Deadlines are <span style=\"color:red\">strict</span>. After the deadline Canvas submission is **closed**. Only the last submission will be graded. \n",
    "6. Deadline for every problem set will be announced at the moment of publishing\n",
    "5. Problem sets will be checked for **plagiarism**. If noticed, the score will be divided by a number of similar works"
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   "source": [
    "## Attendance\n",
    "\n",
    "Attendance is not strict, but **do not disappoint us**. Some lectures will be in the online mode."
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    "## Exam\n",
    "\n",
    "- Classical oral exam with a list of questions ([questions](https://github.com/oseledets/nla2020/blob/master/exam/exam_questions.pdf) from 2020)\n",
    "- **If you fail exam, you get zero for the course**\n",
    "- [The list of questions](https://github.com/oseledets/nla2020/blob/master/exam/teormin.pdf) such that if you can not answer any question from this list during the final exam, you will automatically get **F** for this course. It will be probably updated by the end of November. "
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    "## Projects\n",
    "\n",
    "\n",
    "- We give you time ($\\approx$ one week) and points (15% of your final grade) to test studied methods in real-world problems\n",
    "- We will provide some examples in the second part of this class\n",
    "- For inspiration you can checkout recent conference papers (e.g. [here](https://openreview.net/))\n",
    "- 2–5 students per team\n",
    "- Start thinking about your project topics as early as possible!"
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    "## Grades\n",
    "\n",
    "1. A: 86 - 100 %\n",
    "2. B: 70 - 85 %\n",
    "3. C: 50 - 70 %\n",
    "4. D: 30 - 50 %\n",
    "5. E: 15 - 30 %\n",
    "6. F: 0 - 15 %\n",
    "\n",
    "But they can be slightly adjusted."
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    "## Python 3\n",
    "- We will use Python ecosystem for programming.\n",
    "- Please, follow the rules that will be given in the problem sets"
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    "## Materials\n",
    "\n",
    "**Our materials:**\n",
    "- Lecture notes are avaliable online\n",
    "- Matrix decomposition [cheat sheet](../decompositions.pdf)\n",
    "\n",
    "\n",
    "**If you have difficulties with basic linear algebra:**\n",
    "- [Cheat sheet](http://cs229.stanford.edu/section/cs229-linalg.pdf) with basics\n",
    "- Gilbert Strang book \"Introduction to Linear Algebra\"\n",
    "- Gilbert Strang has [recorded lectures](https://www.youtube.com/watch?v=ZK3O402wf1c&list=PL49CF3715CB9EF31D) on YouTube\n",
    "\n",
    "\n",
    "**Comprehensive NLA books:**\n",
    "- Gene H. Golub, Charles. F. Van Loan, \"Matrix computations\" (4th edition)\n",
    "- Lloyd N. Trefethen and David Bau III, \"Numerical Linear Algebra\"\n",
    "- Eugene. E. Tyrtyshnikov, \"Brief introduction to numerical analysis\"\n",
    "- James W. Demmel, \"Numerical Linear Algebra\"\n",
    "\n",
    "\n",
    "- Many applications of linear algebra you can find in \"[Introduction to\n",
    "Applied Linear Algebra](http://vmls-book.stanford.edu/vmls.pdf)\" by S. Boyd and L. Vandenberghe"
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