Mathematical Methods

Study Course Description

Course Description Statuss:Approved

Course Description Version:5.00

Study Course Accepted:14.03.2024 11:38:29

Study Course Information
Course Code:		SL_105		LQF level:		Level 7
Credit Points:		4.00		ECTS:		6.00
Branch of Science:		Mathematics; Theory of Probability and Mathematical Statistics		Target Audience:		Life Science
Study Course Supervisor
Course Supervisor:		Jeļena Perevozčikova
Study Course Implementer
Structural Unit:		Statistics Unit
The Head of Structural Unit:
Contacts:		23 Kapselu street, 2nd floor, Riga, statistikarsu[pnkts]lv, +371 67060897
Study Course Planning
Full-Time - Semester No.1
Lectures (count)		16	Lecture Length (academic hours)		2	Total Contact Hours of Lectures		32
Classes (count)		8	Class Length (academic hours)		2	Total Contact Hours of Classes		16
Total Contact Hours								48
Part-Time - Semester No.1
Lectures (count)		16	Lecture Length (academic hours)		1	Total Contact Hours of Lectures		16
Classes (count)		8	Class Length (academic hours)		2	Total Contact Hours of Classes		16
Total Contact Hours								32
Study course description
Preliminary Knowledge:
Students must have the necessary mathematical background to understand key statistical techniques and their derivation, if they involve concepts covered in the course. In addition, good knowledge of high school algebra as well as understanding of the notion of a function and its graph.
Objective:
This course aims at providing mathematical background for further calculus-based learning of statistics. The main objective of this course is to allow students to understand mathematical concepts that are necessary to follow proofs and reasoning in subsequent courses. Students are not expected to spend much time understanding proofs of calculus theorems, but rather to build intuition of fundamental ideas of calculus and linear algebra, and their role and application in statistics.
Topic Layout (Full-Time)
No.	Topic			Type of Implementation		Number	Venue
1	Functions and their graphs. Domain and range of the function. Combining functions.			Lectures		1.00	auditorium
				Classes		0.50	computer room
2	Limit of a function, limit laws. The precise definition of a limit.			Lectures		1.00	auditorium
				Classes		0.50	computer room
3	Continuity. Limits involving infinity.			Lectures		1.00	auditorium
				Classes		0.50	computer room
4	Derivative, differentiation rules.			Lectures		1.00	auditorium
				Classes		0.50	computer room
5	The chain rule. Linearization and differentials.			Lectures		1.00	auditorium
				Classes		0.50	computer room
6	Applications of derivatives: extreme values, monotonicity, concavity.			Lectures		1.00	auditorium
				Classes		0.50	computer room
7	Applied optimization problems, Newton’s method to solve equations. Antiderivative.			Lectures		1.00	auditorium
				Classes		0.50	computer room
8	Estimating area with finite sums. Limits of finite sums. Definite integral.			Lectures		1.00	auditorium
				Classes		0.50	computer room
9	The Fundamental theorem of calculus. Indefinite integral.			Lectures		1.00	auditorium
				Classes		0.50	computer room
10	Substitution method for indefinite and definite integral. Applications of definite integral.			Lectures		1.00	auditorium
				Classes		0.50	computer room
11	Other techniques of integration.			Lectures		1.00	auditorium
				Classes		0.50	computer room
12	Infinite sequences and series.			Lectures		1.00	auditorium
				Classes		0.50	computer room
13	Vectors and the geometry of spaces.			Lectures		1.00	auditorium
				Classes		0.50	computer room
14	Matrix, matrix operations.			Lectures		1.00	auditorium
				Classes		0.50	computer room
15	Determinants. Inverse matrix.			Lectures		1.00	auditorium
				Classes		0.50	computer room
16	Eigenvalues, eigenvectors and diagonalization of a matrix.			Lectures		1.00	auditorium
				Classes		0.50	computer room
Topic Layout (Part-Time)
No.	Topic			Type of Implementation		Number	Venue
1	Functions and their graphs. Domain and range of the function. Combining functions.			Lectures		1.00	auditorium
				Classes		0.50	computer room
2	Limit of a function, limit laws. The precise definition of a limit.			Lectures		1.00	auditorium
				Classes		0.50	computer room
3	Continuity. Limits involving infinity.			Lectures		1.00	auditorium
				Classes		0.50	computer room
4	Derivative, differentiation rules.			Lectures		1.00	auditorium
				Classes		0.50	computer room
5	The chain rule. Linearization and differentials.			Lectures		1.00	auditorium
				Classes		0.50	computer room
6	Applications of derivatives: extreme values, monotonicity, concavity.			Lectures		1.00	auditorium
				Classes		0.50	computer room
7	Applied optimization problems, Newton’s method to solve equations. Antiderivative.			Lectures		1.00	auditorium
				Classes		0.50	computer room
8	Estimating area with finite sums. Limits of finite sums. Definite integral.			Lectures		1.00	auditorium
				Classes		0.50	computer room
9	The Fundamental theorem of calculus. Indefinite integral.			Lectures		1.00	auditorium
				Classes		0.50	computer room
10	Substitution method for indefinite and definite integral. Applications of definite integral.			Lectures		1.00	auditorium
				Classes		0.50	computer room
11	Other techniques of integration.			Lectures		1.00	auditorium
				Classes		0.50	computer room
12	Infinite sequences and series.			Lectures		1.00	auditorium
				Classes		0.50	computer room
13	Vectors and the geometry of spaces.			Lectures		1.00	auditorium
				Classes		0.50	computer room
14	Matrix, matrix operations.			Lectures		1.00	auditorium
				Classes		0.50	computer room
15	Determinants. Inverse matrix.			Lectures		1.00	auditorium
				Classes		0.50	computer room
16	Eigenvalues, eigenvectors and diagonalization of a matrix.			Lectures		1.00	auditorium
				Classes		0.50	computer room
Assessment
Unaided Work:
1) Individual work with required and additional literature – careful reading of the chapters corresponding to current topics for each lecture to create theoretical bases. 2) Thorough review of solutions for provided examples to sum up the material for all practical classes. In order to evaluate the quality of the study course as a whole, the student must fill out the study course evaluation questionnaire on the Student Portal.
Assessment Criteria:
1) Practical tasks - 50% 2) Written exam – 50%.
Final Examination (Full-Time):		Exam (Written)
Final Examination (Part-Time):		Exam (Written)
Learning Outcomes
Knowledge:		• the student is able to demonstrate deeper knowledge, understands and explains the concepts of limit, derivative, integral, infinite series; • recognizes and uses the notation of matrices and determinants; • independently utilize basic methods to do computations involving mathematical objects studied in the course; • qualitatively describes examples of the practical application of mathematical objects studied in the course, understands how to use them in the research.
Skills:		• student independently uses limit concept and limit laws to predict the behaviour of a given function; • finds derivative and indefinite integral of a function, computes definite integral; • performs computations with matrices and determinants; • applies rules and methods of mathematical objects studied in the course to solve a practical problem related to these objects.
Competencies:		Students have an comprehension of how calculus generalize pre-calculus mathematics using the limit process and how that can be further integrated to other real-world situations if necessary. Students are competent formulate their tasks into mathematical problems and choose the appropriate method to solve them.
Bibliography
No.	Reference
Required Reading
1	Strang, G. (2006). Linear algebra and its applications. 4th Edition, Brooks Cole.
2	Hass, J., Heil, C., Weir, M. D., & Thomas, G. B. (2018). Thomas' calculus. 14th Edition, Pearson.
Additional Reading
1	Stewart, J. (2016). Calculus: Early Transcendentals. 8th Edition, Cengage Learning.
2	Lay, D. C. (2012). Linear algebra and its applications. Boston: Addison-Wesley.