MATH 425 | Course Introduction and Application Information - Department of Mathematics

Course Name

Mathematical Computing and Simulation I

Code	Semester	Theory (hour/week)	Application/Lab (hour/week)	Local Credits	ECTS
MATH 425	Fall/Spring	3	0	3	6

Prerequisites	None
Course Language	English
Course Type	Elective
Course Level	First Cycle
Mode of Delivery	face to face
Teaching Methods and Techniques of the Course	Problem Solving Lecture / Presentation
National Occupation Classification	-
Course Coordinator	Doç. Dr. Sevin GÜMGÜM
Course Lecturer(s)	Dr.Öğretim Üyesi ÖMÜR SALTIK
Assistant(s)	Arş.Gör. Merve KAHRAMAN ARİMAN Arş.Gör. SILA SELENAY KOÇ

Course Objectives	This course aim is to provide the students with the basics of mathematical computing and simulation. Various simulation techniques and numerical methods are discussed in the framework of this course.
Learning Outcomes	The students who succeeded in this course; will be able to solve numerically different types of linear and non-linear equations. will be able to solve numerically and analytically (by MATLAB) differential equations. will be able to find numerically integrals and derivatives. will be able to draw graphs. will be able to generate discrete and continuous random variables. will be able to model different stochastic processes.
Course Description	In this course, the concepts of different computational methods are discussed. Student solve equations numerically and constract plots. As the application to probability theory and statistics, different simulation tethniques are studied.
Related Sustainable Development Goals

Course Category	Core Courses
	Major Area Courses
	Supportive Courses	X
	Media and Management Skills Courses
	Transferable Skill Courses

Week	Subjects	Related Preparation
1	Intro to Data Analysis, Data Scientist's Toolbox, Setup (Colab, IPython). Introduction to Google Colab, Markdown cells, and basic IPython shortcuts.	Python Data Science Handbook (PDSH), Jake VanderPlas. (2016). O′Reilly Media Inc. ISBN: 9781098121211 (Ch-1)
2	Data Structures in Python, Functions, and Libraries. NumPy Arrays: The foundation of data structures. Python lists vs. NumPy arrays.	Python Data Science Handbook (PDSH), Jake VanderPlas. (2016). O′Reilly Media Inc. ISBN: 9781098121211 (Ch-2)
3	Random Data, Distributions, Data I/O, and Manipulation. Random Data, Distributions, Data I/O, and Manipulation	Python Data Science Handbook (PDSH), Jake VanderPlas. (2016). O′Reilly Media Inc. ISBN: 9781098121211 (Ch-2, Ch-3)
4	Control Structures, Conditional Statements. Python Logic: if, elif, else, for loops, and list comprehensions.	Python Data Science Handbook (PDSH), Jake VanderPlas. (2016). O′Reilly Media Inc. ISBN: 9781098121211 (Ch-2)
5	Numerical Descriptive Statistics, Relationships between Variables. Pandas Aggregation: df.describe(), df.mean(), df.corr(), and df.groupby().	Python Data Science Handbook (PDSH), Jake VanderPlas. (2016). O′Reilly Media Inc. ISBN: 9781098121211 (Ch-3)
6	Data Visualization: Basic Plotting Systems. Matplotlib: Creating histograms, scatter plots, and line plots in Colab.	Python Data Science Handbook (PDSH), Jake VanderPlas. (2016). O′Reilly Media Inc. ISBN: 9781098121211 (Ch-4)
7	Advanced Visualization, Tidy Data, and Statistical Graphics. Seaborn: Advanced plotting (the Python equivalent of ggplot2). Heatmaps, Pairplots.	Python Data Science Handbook (PDSH), Jake VanderPlas. (2016). O′Reilly Media Inc. ISBN: 9781098121211 (Ch-4)
8	Midterm
9	Hypothesis Testing: One-Sample Tests. SciPy Stats: stats.ttest_1samp. Understanding p-values in Python.	Python Data Science Handbook (PDSH), Jake VanderPlas. (2016). O′Reilly Media Inc. ISBN: 9781098121211 (Ch-4)
10	Checking Assumptions & Goodness of Fit. Normality & Variance: stats.shapiro, stats.levene, and stats.chisquare.	Python Data Science Handbook (PDSH), Jake VanderPlas. (2016). O′Reilly Media Inc. ISBN: 9781098121211 (Ch-4, Ch-5)
11	Simple Linear Regression and Correlation. Scikit-Learn / Statsmodels: Building a linear model and interpreting coefficients.	Python Data Science Handbook (PDSH), Jake VanderPlas. (2016). O′Reilly Media Inc. ISBN: 9781098121211 (Ch-5)
12	Dynamic Reporting (Notebooks). Google Colab as a Report: Integrating LaTeX formulas, images, and text into a final report.	Python Data Science Handbook (PDSH), Jake VanderPlas. (2016). O′Reilly Media Inc. ISBN: 9781098121211 (Ch-1)
13	Data Mining & Statistical Learning (Supervised/Unsupervised). Machine Learning: Intro to Scikit-Learn. K-Means (Unsupervised) and Decision Trees (Supervised).	Python Data Science Handbook (PDSH), Jake VanderPlas. (2016). O′Reilly Media Inc. ISBN: 9781098121211 (Ch-4)
14	Data Mining & Statistical Learning (Supervised/Unsupervised). Machine Learning: Intro to Scikit-Learn. K-Means (Unsupervised) and Decision Trees (Supervised).	Python Data Science Handbook (PDSH), Jake VanderPlas. (2016). O′Reilly Media Inc. ISBN: 9781098121211 (Ch-4)
15	Semester Review
16	Final Exam

Course Notes/Textbooks

Jake VanderPlas. (2016). Python Data Science Handbook (PDSH). O′Reilly Media Inc. ISBN: 9781098121211

Suggested Readings/Materials

1- Molin, S. (2021). Hands-On Data Analysis with Pandas: A Python data science handbook for data collection, wrangling, analysis, and visualization. Packt Publishing Ltd. ISBN: 978-1800563452.

2- McKinney, W. (2012). Python for Data Analysis (3rd ed.). O′Reilly Media, Inc. ISBN: 978-1491957660.

Semester Activities	Number	Weigthing
Participation
Laboratory / Application
Field Work
Quizzes / Studio Critiques
Portfolio
Homework / Assignments
Presentation / Jury	1	10
Project	1	10
Seminar / Workshop
Oral Exams
Midterm	1	30
Final Exam	1	50
Total

Weighting of Semester Activities on the Final Grade	3	50
Weighting of End-of-Semester Activities on the Final Grade	1	50
Total

Semester Activities	Number	Duration (Hours)	Workload
Theoretical Course Hours (Including exam week: 16 x total hours)	16	3	48
Laboratory / Application Hours (Including exam week: '.16.' x total hours)	16		0
Study Hours Out of Class	14	3	42
Field Work			0
Quizzes / Studio Critiques			0
Portfolio			0
Homework / Assignments			0
Presentation / Jury	1	10	10
Project	1	10	10
Seminar / Workshop			0
Oral Exam			0
Midterms	1	30	30
Final Exam	1	40	40
		Total	180

#	Program Competencies/Outcomes	* Contribution Level
#	Program Competencies/Outcomes	1	2	3	4	5
1	To be able to have a grasp of basic mathematics, applied mathematics or theories and applications of statistics.	-	-	-	-	X
2	To be able to use advanced theoretical and applied knowledge, interpret and evaluate data, define and analyze problems, develop solutions based on research and proofs by using acquired advanced knowledge and skills within the fields of mathematics or statistics.	-	-	X	-	-
3	To be able to apply mathematics or statistics in real life phenomena with interdisciplinary approach and discover their potentials.	-	-	X	-	-
4	To be able to evaluate the knowledge and skills acquired at an advanced level in the field with a critical approach and develop positive attitude towards lifelong learning.	-	-	-	-	-
5	To be able to share the ideas and solution proposals to problems on issues in the field with professionals, non-professionals.	-	-	-	-	-
6	To be able to take responsibility both as a team member or individual in order to solve unexpected complex problems faced within the implementations in the field, planning and managing activities towards the development of subordinates in the framework of a project.	-	-	-	-	-
7	To be able to use informatics and communication technologies with at least a minimum level of European Computer Driving License Advanced Level software knowledge.	-	-	-	X	-
8	To be able to act in accordance with social, scientific, cultural and ethical values on the stages of gathering, implementation and release of the results of data related to the field.	-	-	-	-	-
9	To be able to possess sufficient consciousness about the issues of universality of social rights, social justice, quality, cultural values and also environmental protection, worker's health and security.	-	-	-	-	-
10	To be able to connect concrete events and transfer solutions, collect data, analyze and interpret results using scientific methods and having a way of abstract thinking.	-	-	-	-	-
11	To be able to collect data in the areas of Mathematics or Statistics and communicate with colleagues in a foreign language.	-	-	-	-	-
12	To be able to speak a second foreign language at a medium level of fluency efficiently.	-	-	-	-	-
13	To be able to relate the knowledge accumulated throughout the human history to their field of expertise.	-	-	-	-	-