[2019SMAT102] Videos for AM-GM inequality, inequality and set related proofs

I made several videos explaining a few topics that we cover in this course. Some of them came up during my office hours. If you’d like me to explain a certain concept/question covered in our course, feel free to drop me an email and you might see it here 🙂

  1. AM-GM inequality: the statement, how to prove it and its application.

2. Given x > y >z, prove xy+yz > \frac{(x+y)(y+z)}{2}.

3. If  A \cup B \subseteq C \cup D, A \cap B = \Phi, C \subseteq A , then  B \subseteq D.

[BAB210] Business Statistics

I’m teaching this course during the summer semester at Seneca College. The course outline can be found here:


We are into our second half of the semester now and being able to use Excel is an important part for the successful completion of it. I made several short videos explaining how to use certain built-in functions in Excel. More will be coming up as our course progresses.

  1. How to draw a bar chart for categorical data:

2. How to build frequency distribution table and draw histogram:

3. How to do cross tabulation:

4. How to use descriptive states tool in Excel:

5. Excel functions to find mean, median, mode,variance and standard deviation:

6. How to find covariance and correlation for two sets of data:

7. How to draw a box plot:

8. How to draw comparative box plot:

9. Continuous Probability Distributions part I:

10. Continuous Probability Distribution II:

11. how to select random samples

12. How to construct confidence interval for a population mean with population  \sigma known:

13. How to construct confidence interval for a population mean with population  \sigma unknown:

14. How to construct confidence interval for a population proportion:

15. Hypothesis Testing of population mean with  \sigma known: H_0: \mu=295, H_a: \mu \neq 295: two-tail test

16. Hypothesis Testing of population mean with  \sigma unknown: H_0: \mu \leq 7, H_a: \mu > 7: upper tail test

17. Hypothesis Testing of population proportion: H_0: p \leq 0.20, H_a: p 0.2 7: upper tail test

18. Regression Analysis:

[2019SMAT102] A letter to my students

Dear all,
Welcome to the Introduction of Mathematics Proof!
We want your experience this semester to be successful and rewarding. Math 102 is a challenging course that demands consistent hard work throughout the semester. Here are some tips for you to succeed in this course and some common mistakes you want to avoid.
• Expecting to be graded in the same way as high school
In a university level math course, your grade is based primarily on tests. You cannot pass this course without achieving passing grades on tests. The only way to do this is to master the skills and concepts through careful completion of the homework exercises, review of the textbook and class notes, and extra practice whenever needed. If you get a low grade on any quiz or test, you are in danger of not passing. See your instructor immediately for tips on improving.

• Mistaking recognition for mastery
Students think that because they’ve seen the material before, they “know it”. This can lead to laziness at the beginning of the semester. Many students wait until they get a poor grade on a quiz or test before they get serious about the course. By then, it may be too late. Work hard from the first day to avoid this. Remember, you only “know it” if you can do it. This means you must be able to write out correct solutions for every homework exercise without referring to your textbook or notes.

• Believing that with mathematics, you either “get it” or you don’t
This is a myth. Every student can have success in mathematics with enough hard work. How much depends on the individual’s background and experience. However, it is important to realize that you can earn the grade you want with sufficient hard work.

• Not setting aside enough time for homework
Many students are over-committed with work, school, and family responsibilities. Without time to devote to homework and studying you cannot learn mathematics. You must adjust your schedule to allow sufficient time for your math class. While there are some classes where you might be able to take shortcuts, mathematics is not one of them. If you don’t have a minimum of 15 hours per week to study outside of class, you are setting yourself up for failure.

• Misunderstanding how mathematics is learned
Learning algebra involves skill acquisition. It is analogous to the physical training involved in music and sports. You would never expect to learn to play piano by going to a concert two or three times a week. Likewise, you should not think you have learned some mathematics just because you went to class and understood your instructor. Your real learning begins when you try to do the homework exercises on your own. You have “learned” a section of material only when you can write out the solutions to all the homework exercises without aid from your textbook or notes.

• Not addressing lack of preparation
College Algebra is Pre-Calculus (without trigonometry). It is expected that you have a working knowledge of Algebra 2 from high school, or Intermediate Algebra from a community college. If you don’t, you must get to work immediately to fill in the gaps. There are many resources at your disposal to help you review. Use them! Your instructor will describe all of the available options.

Have a great semester!