Course Computational Mathematics

Course Description

This course examines mathematical applications integrated with computer programming. Applications of mathematics in the field of Computer Science include digital images, digital signals, video, predictions and data science. Application of eigenvalues, eigenvectors, for file/image compression, and also for feature extraction for simple problems in data science. Fourier Transformation, Wavelet Transformation, Noise Reduction, prediction, basic concepts of classification and clustering, their application to surrounding problems, especially related to bio-maths, is studied. This course is project-based, so students are asked to apply what they learn to existing problems around them.

Program Objectives (PO)

Mahasiswa mampu menerapkan prinsip-prinsip logika dasar, seperti proposisi, implikasi, dan bikondisional, dalam menyusun dan menginterpretasikan kondisi analisis data yang akurat dan sistematis
Mahasiswa mampu menggunakan konsep himpunan, termasuk operasi dasar, himpunan bagian, dan partisi, dalam proses pengelompokan dan klasifikasi data yang beragam

Mahasiswa mampu memodelkan hubungan data menggunakan matriks dan relasi, termasuk relasi kesetaraan dan relasi pengurutan, untuk memudahkan analisis keterkaitan data
Mahasiswa mampu menerapkan induksi matematik dan fungsi rekursif dalam menganalisis dan membuat model prediktif yang sederhana, yang dapat digunakan dalam penarikan kesimpulan berbasis data
Mahasiswa mampu merancang algoritma sederhana yang efisien, memahami notasi algoritmik, dan menerapkannya dalam proses pengolahan data guna meningkatkan efisiensi waktu dan performa analisis data

Aktifitas Pembelajaran

Pertemuan 1

Lecture contract, assessment rubric., introduction to the theory of computational mathematics using Python., Propositions., Combining Propositions., Truth Tables., Exclusive Disjunction.

Date 26 Agustus 2025

Pertemuan 2

Laws of Propositional Logic., Logical Operations in Computers., Conditional Propositions (Implications)., Variants of Conditional Propositions.

Date 2 September 2025

Pertemuan 3
Biconditional (Bi-implication)., Inference., Arguments., Axioms., Theorems, Lemmas, and Corollaries.
Date 9 September 2025
Pertemuan 4
Definition of Sets., Representation of Sets., Cardinality., Empty Set., Subsets., Equal Sets.
Date 16 September 2025
Pertemuan 5
Equivalent Sets., Disjoint Sets., Power Sets., Operations on Sets.
Date 23 September 2025
Pertemuan 6
Extension of Set Operations., Laws of Sets., Principle of Duality., Principle of Inclusion-Exclusion.
Date 30 September 2025
Pertemuan 7
Partition., Proof of Set Propositions., Multisets., Set Type in Pascal Language., Introduction to Logic and Fuzzy Sets.
Date 7 Oktober 2025
Pertemuan 8
Midterm Exam (UTS)
Date 14 Oktober 2025
Pertemuan 9
Matrices., Relations., Representation of Relations with Tables., Matrices., and with Directed Graphs.
Date 21 Oktober 2025
Pertemuan 10
Inverse Relations., Combining Relations., Composition of Relations., Properties of Relations., Equivalence Relations.
Date 28 Oktober 2025
Pertemuan 11
Partial Order Relations., Closure of Relations., N-ary Relations., Functions.
Date 4 November 2025
Pertemuan 12
Inverse Functions., Composition of Functions., Some Special Functions., Recursive Functions.
Date 11 November 2025
Pertemuan 13
Statements Regarding Integers., Simple Induction Principle., Extended Induction Principle.
Date 25 November 2025
Pertemuan 14
Strong Induction Principle., General Form of Induction.
Date 2 Desember 2025
Pertemuan 15
Algorithms., Notation for Algorithms., Some Examples of Algorithms., Integers.
Date 9 Desember 2025
Pertemuan 16
Final Exam (UAS)
Date 16 Desember 2025