# Mathematics

for

Managerial, Life and Social Sciences

Undergrad ePrep Course

Available at SF@NS

Mathematics is a fundamental subject that plays a significant role in our academic studies, whether we realize it or not. It provides us with tools to analyze and solve complex problems and helps us to make informed decisions. However, despite its importance, many students tend to overlook mathematics in their preparation for university studies. If you’re a student about to embark on your university studies, here’s why you should consider studying mathematics and how it can benefit you in the long run.

Firstly, mathematics is essential for a wide range of fields, including science, engineering, economics, and finance. As such, studying mathematics can open up various career opportunities for you. A solid foundation in mathematics can prepare you for for your studies in the universities, and many lucrative jobs that require advanced problem-solving skills.

Secondly, mathematics can help you develop critical thinking skills, which are crucial for success in any field of study. It teaches you how to analyze information, make logical conclusions and solve problems systematically. These skills are transferable and can be applied to many real-life situations, making you a more effective problem solver.

Moreover, studying mathematics can improve your overall academic performance. Mathematics is a subject that requires strong basic understandings and consistent practice, and by engaging in regular math practice, you’ll develop discipline and focus that can help you in your other courses. Many students who excel in mathematics have reported that their overall academic performance improved significantly as a result.

Lastly, studying mathematics can be fun and intellectually stimulating. Mathematics is a beautiful subject that can help you to develop an appreciation for patterns, logic, and symmetry and solve problems that you thought could not be solved. It can provide you with a sense of accomplishment when you solve a difficult problem or discover a new principle.

Studying mathematics is essential for any student who wants to excel academically and professionally. It provides you with invaluable skills, a wide range of career opportunities, and an intellectual challenge that can be both rewarding and enjoyable. Don’t overlook the importance of strengthening mathematics to prepare for your university studies, and do consider taking this eprep course “Mathematics for Managerial, Life and Social Sciences” by NTU. The rewards are undoubtedly worth the effort.

Mathematics for Managerial, Life and Social Sciences is one of the ten specially designed ePrep courses, meant to help NSFs, NSmen and others to better prepare themselves for university studies, whether in a local university in Singapore, or in a university overseas.

A significant factor that contributes to poor academic performance in universities is a lack of understanding in mathematics. This applies to students across all fields of study, not just those in engineering and physical sciences. In fact, studies have shown that even students in managerial, life, and social sciences, and many other fields, can struggle if they lack adequate comprehension of mathematics. Therefore, it is crucial to develop strong mathematical skills to excel academically in any field of study.

This Mathematics for Managerial, Life and Social Sciences ePrep course is developed in collaboration with the publishers of the textbook, Applied Mathematics for Managerial, Life and Social Sciences by Soo T Tan. The textbook comes free with the course, together with lots of good learning materials provided by the publishers. You can see some samples materials below. After studying this course, you will have built a strong foundation in mathematics that will enable you to deal with the mathematical requirement of your university studies.

Please note that this course, as well as the other ePrep courses provided by NTU, will soon also be available at SF@NS LXP, the SkillsFuture@National Service Learning eXperience Platform.

**Main Course Contents**

FUNDAMENTALS OF ALGEBRA.

FUNCTIONS AND THEIR GRAPHS.

EXPONENTIAL AND LOGARITHMIC FUNCTIONS.

MATHEMATICS OF FINANCE.

SYSTEMS OF LINEAR EQUATIONS AND MATRICES

LINEAR PROGRAMMING.

SETS AND PROBABILITY.

ADDITIONAL TOPICS IN PROBABILITY.

THE DERIVATIVE.

APPLICATIONS OF THE DERIVATIVE.

INTEGRATION.

CALCULUS OF SEVERAL VARIABLES.

The details of the topics are given here.

Learning materials for all chapters are provided, but for the purpose of certification, a student has to pass the tests for the first three chapters and any other three from the remaining nine chapters.

### What You Get in this Mathematics Course

**I. Free Textbook**

##### “Applied Mathematics for Managerial, Life and Social Sciences” is a very popular mathematics textbook for those doing managerial, life or social sciences degrees.

**II. Free Consultation**

##### A retired NTU professor is acting as the tutor. You can consult him via email or WhatsApp, even beyond the official course duration.

**III. Materials Online**

##### 1 PowerPoint and video files.

##### 2 Answers/solutions to all questions/problems in the textbook.

##### 3 Online exercises.

##### 4 Problems and solutions in files.

##### 5 Bonus learning materials in geometry, trigonometry, discrete mathematics and economics are included.

##### 6 Samples of main course materials and bonus course materials are provided below.

**IV. Digital Certificate**

##### A digital certificate will be issued if you have successfully completed this ePrep course and passed all the tests at the end of each of the ten compulsory chapters.

**Samples of Mathematics Course Materials**

**1. Video Lesson** (Logarithmic Function)

*This short video lesson illustrates the relationship between base and exponent and the resulting number expressed in exponential form or logarithmic form.*

**2. Question and Answer** (Linear Programming)

**Question**: A financier plans to invest up to $500,000 in two projects. Project A yields a return of 10% on the investment whereas project B yields a return of 15% on the investment. Because investment in project B is riskier than the investment in project A, the financier has decided that the investment in project B should not exceed 40% of the total investment. How much should she invest in each project in order to maximize the return on her investment?

**Answer**: Let *x* and *y* denote the amount (in thousands of dollars) to be invested in project A and project B, respectively. Since the amount available for investment is up to $500,000, we have

* x* + *y* *≤ *500

Next, the condition on the allocation of the funds implies that

y *≤ *0.4(*x *+ *y*), –0.4*x* + 0.6*y ≤ *0*, *or –2*x* + 3*y* *≤ *0

The linear programming problem at hand is

Maximize *P* = 0.1*x* + 0.15*y* subject to

* x* + *y* *≤ *500

–2*x* + 3*y* *≤ *0

*x* ≥ 0, *y* ≥ 0

**Samples of Bonus Materials**

**1. Economics** (Costs in the Short Run and in the Long Run)

1. The division of total costs into fixed and variable costs will vary from firm to firm

- Some costs are fixed in the short run, but all are variable in the long run.
- For example, in the long run, a firm could choose the size of its factory.
- Once a factory is chosen, the firm must deal with the short-run costs associated with that plant size.

2. The long-run average-total-cost curve lies along the lowest points of the short-run average-total-cost curves because the firm has more flexibility in the long run to deal with changes in production.

3. The long-run average total cost curve is typically U-shaped, but is much flatter than a typical short-run average-total-cost curve.

4. The length of time for a firm to get to the long run will depend on the firm involved.

5. Definition of **the**** short-run**: the period of time in which some factors of production cannot be changed.

6. Definition of **the long-run: **the period of time in which all factors of production can be altered.

**2. Discrete Mathematics** (Recurrence Relation)

**Question:**

**Solution:**

**Remarks**

##### These are some samples of the bonus materials on economics and discrete Mathematics.

##### Remember not to short-change yourself – do not go for any of those low-grade courses prepared by any “Tom-Dick-And-Harry” who self-claim to be an industry expert or mathematics expert, especially if you are preparing for academic university studies or career advancement! You also get a hard copy “Applied Mathematics for the Managerial, Life and Social Sciences” textbook.

##### Go only for a high-quality specially-designed academic course such as this Mathematics e_prep course for getting you a head start in university, or in your career.

##### We also have two more advanced specialized mathematics courses if you need them:

##### 1. Engineering Mathematics – Calculus which provides a very comprehensive and advanced coverage on *calculus*.

##### 2. Statistics for Undergraduate Studies – which provides a more comprehensive and advanced coverage on *probability and statistics*.

**Example Applications of Mathematics in Various Fields**

Here are some examples of applications of mathematics:

**Applications of Exponential and Logarithmic Functions to Solve Growth Problems**

- level of absorption of drugs
- forensic science to determine time of death
- growth of population, tumor, bacteria
- spread of diseases
- effect of advertisement on sales

**Applications of Linear Programming to Solve Optimization Problems**

- Social program planning
- advertising
- investment-asset allocation
- agriculture-crop planning
- nutrition planning

**Applications of Functions and Their Graphs**

Deb Farace of Pepsico testified that she shared the mathematical model on how sale is impacted by weather with buyers and resulted in increase in sale because the buyers were able to better place buy orders according to demand due to different weather conditions.

**Applications of Derivatives**

Richard Mizak of Kroll Zollo Cooper testified that he used mathematical models to help distressed companies to improve their operations.

**Who should take this ePrep course on Mathematics for Managerial, Life and Social Sciences?**

##### Mathematics is a must-do course for almost all students as most students do not have a strong foundation in mathematics and weakness in mathematics is often the obstacle to proper learning and understanding the depth of a principle!

##### Even for those not going to any university due to various reasons, this is an opportunity to enhance their mastery of the many mathematical concepts involved in the issues they face, and to prove that they are capable of completing a university-level course. A certificate may come in handy when applying for a job.

##### Everyone is welcome and there is no pre-requisite as there are introductory materials and also we will provide the necessary guidance for those who need it.

**How to Sign Up?**

**1 For NSFs **

There are Two Ways

There are Two Ways

**i. SF@NS Scheme**

##### Activate your SF@NS LXP Account at https://go.gov.sg/activatesfnslxp, then sign up for this and other ePrep Courses by NTU. There is no limit to the number of courses you can sign up for.

**ii. NS e_PREP Scheme**

##### Please sign up via **NS Portal**. Select “Acess ePREP”, then search for NTU as the Course Provider. Pick the course “Mathematics for Managerial, Life and Social Sciences” from among the NTU’s e-PREP courses listed.

2 Non-NS folks

2 Non-NS folks