In this Integral Calculus course, various integration techniques will be studied. Some of the integration techniques discussed in this course are the substitution method, partial integrals, rational broken integrals and trigonometric function methods. The solution of definite integrals with the fundamental theorem of calculus will also be studied. The solution of improper integrals will also be discussed in this lecture chapter. The final material will concentrate on the application of definite integrals such as calculating the area between curves, the volume of rotating objects and the length of curves. The discussion of the application of definite integrals includes cases in Cartesian and polar coordinates.

[1]. Prihandono, Bayu.2023. Kalkulus Integral (Konsep dan Aplikasinya). Pontianak: UNTAN Press
[2]. Stewart, J. 2001. Kalkulus. 4th ed. I Nyoman Susila & Hendra Gunawan, penerjemah. Jakarta: Erlangga.
[3]. Varberg, Purcell, E. Purcell & S. Rigdon.2006. Calculus. 9th ed. Boston: Prentice Hall

This course covers the basics of mathematics, including number systems, inequalities, absolute values, functions, limits, continuity, derivatives and its application to optimization problems. The course places a particular emphasis on the counting aspect.

1. Purcell, E. J. & Varberg, D., 1994. Kalkulus dan Geometri Analitis. 4th Ed. I Nyoman Susila, Bana Kartasasmita, Rawuh, penerjemah. Jakarta: Erlangga.
2. Stewart, J. 2001. Kalkulus. 4th Ed. I Nyoman Susila & Hendra Gunawan, penerjemah. Jakarta: Erlangga.
3. Varberg, D., Purcell, E.J., & Rigdon, S.E. 2007. Calculus. 9th ed. Boston: Prentice Hall, Inc.
4. Noviani, E., Helmi, Kiftiah, M., & Yudhi. 2021. Kalkulus 1. Pontianak: Untan Press.

In general, this course discusses aspects related to the way of thinking using mathematical principles and aspects related to sets. These aspects include, the basics of mathematical logic, quantification, proof techniques, inference methods in mathematics, set basics, set families, ordered sets and set relations.

1. Devlin, K., 1992. Sets, Function and logic, 2nd edition. New York: Chapman and Hall.
2. Soehakso, R., 1993. Pengantar Matematika Modern. 1st edition. Yogyakarta: Jurusan Matematika FMIPA.
3. Sundstrom, T., 2014, Mathematical Reasoning Writing and Proof, Grand Valley State University.
4. Kusumastuti, N., Prihandono, B, 2023, Bahan Ajar Pengantar Matematika Modern, FMIPA UNTAN

The course Elementary Linear Algebra would likely cover the following topics:

1. Systems of Linear Equations: This includes methods for solving systems of linear equations such as Gaussian elimination, matrix representation of systems, and methods for solving non-square systems.

2.  Matrix Operations: Students would learn about basic operations on matrices including addition, subtraction, scalar multiplication, and matrix multiplication. They would also study properties of matrices under these operations.

3. Determinants and Inverses: The course would cover the concept of determinants and their calculation, including properties and applications. In addition, students would learn about matrix inverses, their existence, and how to find them.

4. Relationships between Solutions of Systems, Matrix Inverses, and Determinants: This aspect would focus on understanding the connections between solutions of systems of linear equations, matrix inverses, and determinants of matrices. This might involve discussing the conditions under which systems have unique solutions, no solutions, or infinitely many solutions.

5. Vector Operations and Properties: Students would learn about operations on vectors such as addition, scalar multiplication, and dot product. They would also study geometric and algebraic properties of vectors in Euclidean spaces.

6. Vector Projections and Applications: This part would involve understanding vector projections onto other vectors and their applications, particularly in problems involving lines and planes in three-dimensional space.

Overall, the course would provide a foundation in basic linear algebra concepts and techniques, essential for understanding more advanced topics in mathematics and various applications in other fields.

1. Anton, H., & Rorres, C. (2004). Aljabar Linear Elementer versi Aplikasi, Edisi Kedelapan. Erlangga.
2. Lipschutz, S., & Lipson, M. (2001). Schaum's outline of theory and problems of linear algebra. Erlangga.
3. Kusumastuti, N., Yundari, Fran, F., Pasaribu, M. 2020. Aljabar Linear Elementer, Bahan Ajar. FMIPA UNTAN

The course material focuses on introducing students to mathematical software, specifically Maple. By utilizing Maple, students are expected to receive assistance in solving complex mathematical problems. Additionally, this software can facilitate simulations during students' thesis or final project work.

Abel, M.L. dan Braselton, J.B. 2005. Maple by Example, 3rd edition, Elsevier Academic Press, USA. 

This course discusses the basic concepts of geometry which include incidence geometry, plane analytic geometry and space analytic geometry. In this course, more emphasis is placed on the calculation aspects and concepts of geometry.

Win J. Purcell, Dale Varbeg, and Steven E. Rigdon, 2003, Calculus 8th Edition,Prentic hall: Addison Wesley

The course will cover the random variable, Special Distribution of Random Variable, Multivariate of random variable, and function of random variable.

1. Bain L Jee and Engekhardt Max, 1992, Introduction to Probability and Mathematical Statistics, second Edition, Duxbury Press:California.
2. E. Walpole, Ronald, H Maiers, Raymon, 1986, Ilmu Peluang dan Staistik untuk Insinyur dan Ilmuwan, second edition, ITB: Bandung.

This Linear Algebra course is a compulsory course in Departement of Mathematics FMIPA Untan which discuss the basics of vector space structure, linear transformations, and inner product spaces.

1. Anton, H. & Rorres, C., 2004, Aljabar Linear Elementer Versi Aplikasi. Jakarta: Erlangga.
2. Fraleigh, J.B., 1994, A first Course in Abstract Algebra, Fifth Edition, Addison-Wesley, New York.
3. Hungerford, T.W., 1974, Algebra, Springer-Verlag, New York.
4. Sukirman dan Soebagio, S., 1994, Struktur Aljabar, FMIPA UNY, Yogyakarta

1. Introduction to Linear Programming: formulate of the Linear Programming model
2. Graphical of Linear Programming solution
3. The simplex Method
4. Infeasible solution, unbounded solutions, degeneracy, alternative solutions
5. Theory of linear programming.
6. Integer Programming: formulate of the Integer linear programming, branch and bound algorithm and cutting plane algorithm.
7. Duality: definition of the dual problem
8. Sensitivity analysis
9. Laboratory work

1. Hillier, F. S., & Lieberman, G. J. (2001). Introduction to Operations Research. New York: McGraw Hill.
2. Pasaribu, M. & Kiftiah, M. 2024. Pemrograman Linear: Seri Metode Grafik dan Metode Simpleks. Pontianak: Untan Press. 
3. Sharma, J. K. (2016). Operations Research Theory and Applications, Sixth Edition. India: Trinity Press.
4. Taha, H. A. (2007). Operations Research: An Introduction, Eight Edition. USA: Pearson Education, Inc.
5. Winston, W. L. (2003). Operations Research Applications and Algorithms, Fourth Edition. United States: Thompson Learning

Based on the provided course objectives, Discrete Mathematics course would typically cover the following topics:

1. Basic Concepts of Integer Systems: This would include fundamental concepts related to integers such as divisibility, prime numbers, modular arithmetic, and congruence.
2. Mathematical Induction: Students would learn about the principle of mathematical induction and its application in proving statements and solving problems involving sequences, series, and recursive definitions.
3. Combinatorial Principles: The course would cover various combinatorial principles such as the Inclusion-Exclusion Principle and the Pigeonhole Principle. Students would learn how to apply these principles to count and solve problems related to combinations, permutations, and counting arguments.
4. Binomial Coefficients and Binomial Theorem: Students would study the properties of binomial coefficients and how to prove their equality. They would also learn about the Binomial Theorem and its applications in expanding binomial expressions and calculating probabilities.
5. Generating Functions: The concept of generating functions would be introduced, focusing on how they can be used to represent combinatorial sequences and solve combinatorial problems.
6. Recurrence Relations: Students would learn about recurrence relations and methods for solving them, including methods such as substitution and characteristic equations. They would also explore applications of recurrence relations in various mathematical contexts.

Overall, the course would provide students with a solid foundation in discrete mathematics, which is essential for understanding and analyzing algorithms, cryptography, combinatorial optimization, and various other areas of computer science and mathematics.

1. Liu, C.L., 1995, Dasar-dasar Matematika Diskret, edisi 2, PT Gramedia Pustaka Utama, Jakarta.
2. Slamet, S., & Makaliwe, H. (1991). Matematika Kombinatorik. Jakarta: PT Elex Media Komputindo. 
3. Rosen, Kenneth H., 2001, Discrete Mathematics and its Applications, 5th edition, Mc Graw Hill, New York.
4. Kusumastuti, N., 2021, Matematika Diskret: Metode-metode Pembuktian, Bahan Ajar, FMIPA UNTAN
5. Kusumastuti, N., 2021, Matematika Diskret: Teori Kombinatorika, Bahan Ajar, FMIPA UNTAN

Multivariable functions and limits (definitions, curve curvature graphs, vector-valued functions, limits and continuity), multivariable derivatives (partial derivatives, gradients, implicit, chain rules), applied derivatives, fold integrals and their applications.

[1].  Prihandono, Bayu.2023. Kalkulus Integral (Konsep dan Aplikasinya). Pontianak: UNTAN Press 

[2].  Stewart, J. 2001. Kalkulus. 4th ed. I Nyoman Susila & Hendra Gunawan, penerjemah. Jakarta: Erlangga.

[3].  Varberg, Purcell, E. Purcell & S. Rigdon.2006. Calculus. 9th ed. Boston: Prentice Hall

[4].  Noviani, E., Helmi, Kiftiah, M., & Yudhi. 2021. Kalkulus 1. Pontianak: Untan Press.

The course will cover the system of complex numbers, function, limit, and theorems on limit of complex function, analytic function, integral of complex function, series of a complex function and residue and pole.

1. Dedy, E. & Sumiaty, E. 2001. Fungsi Variabel Kompleks. Yogyakarta : Jurusan Pendidikan Matematika FMIPA UNY. 
2. Zill, D. G. & Patrick D. S. 2003. A First Course in Complex Analysis With Application. United States. Jones and Bartlett Publishers, Inc.

This course covers the basic concepts and utilization of algorithms and programming languages, providing students with an alternative approach to solving mathematical modeling problems. The emphasis in this course is more on mastering programming language skills.

1. M. Baudin. 2010. Introduction to Scilab. The Scilab Consortium-Digiteo .France. 
2. S.L. Campbell, J-P Chancelier & R. Nikoukhah. 2006. Modeling and Simulation in Scilab/Scicos. Springer, New York 
3. R.A. Sukamto. 2018. Logika dan Pemrograman Dasar. Penerbit Modula, Bandung. 

The course will cover the system of real numbers, sequences, and series, including their convergence.

1. Bartle, R. G., and Sherbert, D. R., (2000), Introduction to Real Analysis, John  Wiley & Sons, third edition, New York"
2. Darmawijaya, Soeparna, (2006), Pengantar Analisis Real, Jurusan Matematika FMIPA UGM, edisi pertama"
3. Kiftiah, Mariatul & Pasaribu, Meliana. Bahan Ajar Pengantar Analisis Real. FMIPA UNTAN

The course will study the theory of limit, continuous and differentiable functions of one real variable introduced in Calculus. It places the familiar techniques of differentiation, such as the Chain Rule, on a firm theoretical foundation and proves some of the key results of real analysis such as the Intermediate Value Theorem, the Mean Value Theorem and Taylor’s Theorem. The basic theory of Riemann integration is also studied.

1. Bartle, R.G and Sherbert, D.R. 2011. Introduction to Real Analysis, 4th ed. United. States: John Wiley & Sons, Inc.
2. Trench, W.F. 2003. Introduction to Real Analysis. New Jersey: Pearson.
3. Darmawijaya, S. 2006. Pengantar Analisis Real. Yogyakarta: Jurusan Matematika FMIPA UGM.

1. Model, application, and algorithm for transportation, transshipment, assignment. 
2. Network models : shortest path problem, minimum spanning tree, maximum flow, traveling salesman problem, and critical path method
3. Laboratory work

1. Hillier, F. S., & Lieberman, G. J. (2001). Introduction to Operations Research. New York: McGraw Hill.
2. Prihandono, B. & Pasaribu, M. Modul Ajar Riset Operasi. Pontianak: FMIPA UNTAN
3. Sharma, J. K. (2016). Operations Research Theory and Applications, Sixth Edition. India: Trinity Press.
4. Taha, H. A. (2007). Operations Research: An Introduction, Eight Edition. USA: Pearson Education, Inc.
5. Winston, W. L. (2003). Operations Research Applications and Algorithms, Fourth Edition. United States: Thompson Learning

Research Methodology in Mathematics equips students with the essential skills and knowledge required to undertake research effectively in the field of mathematics. Through this course, students will learn the fundamental steps involved in conducting research, including research design, literature review, data collection, analysis, and presentation. Additionally, students will gain proficiency in utilizing various tools and software for word processing, data analysis, and reference management.

Through interactive lectures, practical exercises, and hands-on projects, students will develop the necessary skills and competencies to undertake independent research in mathematics successfully. Additionally, discussions on ethical considerations in research and effective communication of research findings will be integrated throughout the course to foster responsible and impactful research practices.

1. Creswell, John W, Research Design (1994). Qualitative and Quantitative Approaches, London : SAGE Publication. 
2. Buku Pedoman Penulisan Tugas Akhir Jurusan Matematika FMIPA Universitas Tanjungpura
3. Halmos, P. R. (1970). How to write mathematics. L’enseignement mathématique, 16(2), 123-152.
4. Gillman, L. (2022). Writing mathematics well: a manual for authors. American Mathematical Society.

1. Statistics, data, and probability
2. Sampling distribution, estimation, and hypothesis test 
3. Laboratory work

1. Kusnandar, D., Debataraja, N.N., Mara, M.N., dan Satyahadewi, N. 2019. Metode Statistika serta Aplikasinya dengan Minitab, Excel dan R. Untan Press, Pontianak.
2. Weiss, N.A, 2012. Introductory Statistics. 9th Edition. Addison-Wesley, Boston, United States of America.

1. Types of insurance
2. Life table
3. Survival function
4. Simple rate
5. Compound rate
6. Anuity
7. Portofolio
8. Introduction to stochastics process

1. Bowers, Newton L, et al., 1997. Actuarial Mathematics. Second Edition. Schumburg, Illinois: The Society of Actuaries.
2. Futami, Takashi., 1993. Matematika Asuransi Jiwa. Jilid I. Gatot Herliyanto, penerjemah. Tokyo: OLICD Centre.
3. Sidi, Pramono dan Malau, R Alam, 2006. Matematika Finansial. Jakarta: Universitas Terbuka.

The course Introduction to Abstract Algebra would likely cover the following topics:
Algebraic Systems: This topic introduces the foundational concepts and structures of algebraic systems, which serve as the basis for abstract algebra. It may cover basic operations, properties, and axioms that algebraic systems follow.
Group and its properties: This topic delves into the theory of groups, which are algebraic structures consisting of a set and a binary operation that satisfies certain properties. Students would study group axioms, group operations, subgroup structure, and properties of groups.
Quotient Groups and Group Homomorphisms: This topic explores quotient groups, which are formed by partitioning a group by a normal subgroup, and group homomorphisms, which are functions between groups that preserve the group structure. Students would learn about the properties and applications of quotient groups and group homomorphisms.
Ring, Types, and Characteristics of Rings: This topic introduces rings, which are algebraic structures that generalize the concept of arithmetic operations beyond addition and multiplication. It may cover different types of rings such as commutative rings, integral domains, and fields, as well as characteristics of rings such as the characteristic of a ring.
Subring and Ideal: This topic focuses on subsets of rings that retain the ring structure under the same operations. Students would study subrings, which are subsets of rings that form rings themselves, and ideals, which are special subrings that have additional closure properties under multiplication by elements of the ring.
Quotient Rings and Ring Homomorphisms: Similar to quotient groups, this topic explores quotient rings, which are formed by partitioning a ring by an ideal, and ring homomorphisms, which are functions between rings that preserve the ring structure. Students would learn about the properties and applications of quotient rings and ring homomorphisms.
Overall, the course would provide students with a solid foundation in abstract algebra, equipping them with the necessary tools to understand, analyze, and apply algebraic structures in mathematics and related fields.
Quotient Rings and Ring Homomorphisms: Similar to quotient groups, this topic explores quotient rings, which are formed by partitioning a ring by an ideal, and ring homomorphisms, which are functions between rings that preserve the ring structure. Students would learn about the properties and applications of quotient rings and ring homomorphisms.
Overall, the course would provide students with a solid foundation in abstract algebra, equipping them with the necessary tools to understand, analyze, and apply algebraic structures in mathematics and related fields.

1. Kusumastuti, N. Fran, F., 2023, Pengantar Aljabar Abstrak: Teori Grup dan Ring, Pontianak: UNTAN-Press.
2. Malik, D.S., John N. Mordeson, M.K. Sen 2007, Introduction to Abstract Algebra, Nebraska: Creighton University.
3. Fraleigh, J.B., 1994, A First Course in Abstract Algebra, Fifth Edition,  New York: Addison-Wesley.
4. Hungerford, T.W., 1974, Algebra, New York: Springer-Verlag.

In the course of Ordinary Differential Equation, various techniques will be studied to solve the ODE problems. 

Introduction to Differential Equations: 

• Definition of differential equations
• Classification: ordinary vs. partial, order, linearity, degree
• General solution: definition and examples
• Particular solution: definition and examples
• Singular solution: explanation and examples
• Methods for solving differential equations
• Forming differential equations from given conditions or problems

1. First-Order Ordinary Differential Equations
   • Introduction to first-order ODEs
   • Separable equations
   • Exact equations and integrating factors
   • Linear equations: integrating factor method
   • Bernoulli equations
   • Applications and modeling
2. Homogeneous Linear Equations with Constant Coefficients
   • Homogeneous linear differential equations
   • Characteristic equation and roots
   • Solutions in terms of exponentials
   • Complex roots: Euler's formula
   • Systems of linear differential equations
   • Applications in physics and engineering
3. Homogeneous Linear Equations with Variable Coefficients
   • Introduction to variable coefficients
   • Power series solutions
   • Frobenius method for equations with regular singular points
   • Bessel's equation and Bessel functions
   • Applications in mechanics, electromagnetism, and heat transfer
4. Linear Differential Equations of Degree-n and Laplace Transformation
   • Introduction to Laplace transformation
   • Laplace transform of standard functions
   • Properties of Laplace transforms
   • Inverse Laplace transform
   • Solving linear differential equations using Laplace transforms
   • Application to circuit analysis, control systems, and signal processing

These topics cover a comprehensive understanding of ordinary differential equations, ranging from basic concepts to advanced techniques, along with practical applications across various fields of science and engineering.

1. Ross L Shepley , 1984., Differential Equations., Third edition, Jhon Wiley & Son, Singapure. 
2. Ayres Frank Jr, Ault J.C.,1992. “Teori Dan Soal Persamaan Diferensial “ (terjemahan) Seri Schaum, Cetakan ketiga, Erlangga Jakarta 
3. Finizio. N, G. Ladas., 1988, “ Persamaan Diferensial Biasa Dengan Penerapan Modern”. (Terjemahan). Edisi kedua, Erlangga . Jakarta. 
4. Kreyzig Erwin, 1988 , “Advanced Engineering Mathematics”., Sixth Edition, John Wiley & Sons. New York Chcherster Bribane, Toronto Singapure.