### Introduction to Mathematics (BS zoology semester-1 (URCM-5101))

Zoologists use calculus, statistics and other mathematics for data analysis and modeling. Mathematical approaches use to explore novel and rewarding problems in zoology (see for instance, https://www.zoo.ox.ac.uk/mathematical-ecology-research-group) and the most notable effect of mathematics on zoology would be on population dynamics. This course is built upon the mathematical concepts, principles and techniques that are useful in almost all undergraduate programs. The main objectives of the course are to enhance student’s competency in application of mathematical concepts in solving problems and to improve their level of quantitative approach. Upon the successful completion of this course students would be able to develop understanding: Mathematical functions, Building and solving linear and quadratic equations, Matrices and Determinants with application, sequences and series, and basic Financial Mathematics. To prepare the students, not majoring in mathematics, with the essential tools of financial, algebra and geometry to apply the concepts and the techniques in their respective disciplines.

Intended Learning Outcomes: Upon successful completion of the course, a student will be able to:

1. Sketch surfaces using cross-sections and trigonometric concepts; apply the geometrical formulas.
2. Solve simple linear Equations by using different techniques.
3. State the definitions, results and formulae presented in lectures; apply and adapt these to solve suitable problems.
4. Take a function with multiple inputs and determine the influence of each of them separately.

Contents

1. Linear Equations and Quadratic Equations: Formation of Linear equation
2. Solving Linear equation involving one variable
3. Solution of Quadratic equation by factorization method
4. Solution of quadratic equation by square completion methods
7. Sequences and Series
8. Matrices and Determinants: Introduction of matrices
9. Types of matrices
10. Matrix operations
11. Inverse of matrix
12. The determinants and its properties
13. Solution of system of linear equations by determinants: Cramer’s rule, Inverse Matrices Method
14. Mathematics of Finance: Simple interest
15. Compound interest
16. Annuities
17. Sets and Sets Operations
18. Permutation and combinations
19. Introduction to mathematical induction and binomial theorem
20. Basic Concepts of Trigonometry
21. Fundamental Identities of Trigonometry

Recommended Books

1. Frank, S. B. (1993). Applied mathematics for business, economics, and the social sciences (4 th ed.). New York: McGraw-Hill publisher.
2. Nauman, K. (2019). Basic mathematics-I: algebra and trigonometry (2 nd ed.). Lahore: Al-Hassan Pub.

Suggested Books

1. Kaufmann, J. E. (1994). College algebra and trigonometry (3 th ed.). Boston: PWS-Kent Pub. Co.
2. Swokowski, E. W. (1993). Fundamentals of algebra and trigonometry (8 th ed.). Boston: PWS-Kent Pub. Co.

RESEARCH PROJECT /PRACTICALS/LABS/ASSIGNMENTS

Research project/assignment based on introduction to mathematics often involve features which require their solutions can be awarded to students during their course work period. Examples of features are

1. Accelerating and motivating interest to develop logic based on mathematics.
2. Finding applications and implementing by softwares like Maple
3. Improving existing techniques

Assessment Criteria

• Sessional: 20 (Presentation / Assignment 10, Attendance 05, Quiz 05)
• Mid-Term Exam: 30 (or Term Paper)
• Final-Term Exam: 50 (or Viva + online)

Key Dates and Time of Class Meeting

Monday/Tuesday/Wednesday                                                           10:00 -11:00

Commencement of Classes                                                   November 02, 2020

Mid Term Examination                                                            December 14-18, 2020

Final Term Examination                                                          February 08-12, 2021

Declaration of Result                                                              February 19, 2021