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最終更新日：2020/09/11  
筑波大学 教育課程編成支援システム

GB13604 Mathematics for Computer Science

2.0 単位, 3 年次, 秋AB 水5,6
アランニャ, クラウス, 叶 秀彩

授業概要

The course provides an introduction to elementary concepts of mathematics for computer science. Topics include: formal logic notation, induction, sets and relations, permutations and combinations, counting principles, discrete probability.

備考

英語で授業。
オンライン(オンデマンド型)

授業形態

講義及び演習

学位プログラム・コンピテンスとの関係

・汎用コンピテンス
1. コミュニケーション能力
・専門コンピテンス
1. 情報科学を支える基礎知識
5. グローバルな視野とコミュニケーション能力

授業の到達目標(学修成果)

The goal of this course is to provide the student with a wide groundwork of mathematical concepts. This course focus on mathematical topics that are useful to understand computer science theory. In particular, this course focus on teaching techniques for proving theorems in different mathematical fields that are related to computer sciences. This course is fully in English.

キーワード

英語講義, 数論, グラフ論, 統計, 証明方法

授業計画

In 2020, this course will be fully online. Each lecture will be provided as an "on-demand" video that the students can watch at their preferred time. During the regular lecture hours, the teachers will be available for discussion, for helping with the weekly reports, and for answering questions.

第1回What is a proof? Proof Methods (Proof by Contradiction, Proof by Cases). The well ordering principle. Propositions, Logic and Quantifiers. 担当:アランニャ, クラウス
第2回Sets and Proofs. Induction. Relations and Functions. State Machines. 担当:アランニャ, クラウス
第3回Number Theory. GCD. Primality. Euler's Theorem. RSA Algorithm. 担当:アランニャ, クラウス
第4回Graphs. Walks and Paths. Directed Graphs and Scheduling. Partial Orders and equivalences. 担当:アランニャ, クラウス
第5回Graphs. Degrees and Isomorphism. Trees. Coloring and Connectivity. Stable Matching. 担当:アランニャ, クラウス
第6回Sums and Products. Asymptotic. Computational Complexity. 担当:叶 秀彩
第7回Counting. Bijection Rules, Rules for counting set components (cards, dice, etc). Division Rule, Binomial Theorem. Bookkeeper Principle, Pigeonhole Principle. 担当:叶 秀彩
第8回Probability. Discrete Probability: Probability and Counting. Probability Spaces. Infinite Probability Spaces. Conditional Probability. Bayes' Theorem. 担当:叶 秀彩
第9回Probability. Independence and Causality. Random Variables and Random Walks. Expectation and Mean Time to Failure. 担当:叶 秀彩
第10回Advanced topics: Probability Graphs, Google Pagerank Algorithm. Sampling and Confidence. Final Exam Practice. 担当:叶 秀彩

履修条件

成績評価方法

Every week the student has to submit an exercise sheet in English on manaba. The deadline is one week. The final examination cover the entire course, and will be online in 2020. The final grade is composed of the average grade of the exercise sheets (70%) and the final exam (30%). NOTE: The weight of the final exam in 2020 is lower than in regular years because of the online exam.

学修時間の割り当て及び授業外における学修方法

The lecture video will be available on MS streams, and the professors will be available for questions during lecture time on a MS TEAMS call. The student must submit an exercise sheet after every lecture on manaba. The deadline for the exercise sheet is one week, but the student is encouraged to work on the exercise during the lecture time. The student is expected to complement the lecture video and exercise by reading the recommended chapter from the textbook.

教材・参考文献・配付資料等

This class is based on MIT Open Courseware "Mathematics for Computer Sciences Spring 2015". Materials for this course can be found on: https://ocw.mit.edu/courses/electrical-engineering-and-computer-science/6-042j-mathematics-for-computer-science-spring-2015/

1. Eric Lehman, F. Thomson, Albert Meyer,"Mathematics for Computer Science", https://ocw.mit.edu/courses/electrical-engineering-and-computer-science/6-042j-mathematics-for-computer-science-spring-2015/readings/MIT6_042JS15_textbook.pdf

Video lectures will be distributed on MS Streams, and the lecture materials (PDFs, etc) will be distributed on manaba.

オフィスアワー等(連絡先含む)

The professors will be available on MS TEAMS during the regular lecture hours to answer questions. Also, the students can ask questions directly using the TEAMS online channel.

アランニャ, クラウス 木曜2限
SB1012 (Advanced Research Building B / 総合研究棟B) 029-853-6574 23051014 http://conclave.cs.tsukuba.ac.jp/
叶 秀彩 100002460

その他(受講生にのぞむことや受講上の注意点等)

This course covers topics that are similar to "Programming Challenges" (GB21802) from a more theoretical point of view.

他の授業科目との関連

ティーチングフェロー(TF)・ティーチングアシスタント(TA)