What are Career Opportunities if You Are Good in Math? Rafal Kulik Department of Mathematics and Statistics

Transcription

1 What are Career Opportunities if You Are Good in Math? Rafal Kulik Department of Mathematics and Statistics

2 Doing mathematics and statistics means Identifying and solving problems Proving propositions and theorems Analyzing data Identifying patterns Understanding and modelling phenomena Simulating and computing Writing and presenting what you learned

3 What kind of career will I pursue? Teacher Researcher in Academia Statistician and Data Scientist Actuary Analyst: of data, computers, economics, operations Researcher: in industry, government Computer programmer Communications or information security

4 Or maybe a career in Analysis of finance risk Mathematical modeling in Applied sciences (biology, chemistry, engineering) Economics Medicine (epidemiology, physiology, and more) Mathematicians are specialists in problem solving!

5 Mathematics and Statistics lead to some of the best careers! Wall Street Journal reports on Careercast.com 2015: Top jobs in the US (by environment, salary, and job satisfaction): 1- Actuary 3- Mathematician 4- Statistician 6- Data Scientist Payscale.com College Salary Report : The top 40 Bachelor s degrees, ranked by salary expectations, are based on mathematics: engineering, computer science, economics, mathematics, statistics,

6 Where do our students work Government agencies (Statistics Canada, Health Canada, Environment Canada, NAV Canada, Canadian Border and Security Agency); IT companies (BlackBerry, Google, Microsoft) <- Statistics and Data Science Financial industry (TD Canada, Bank of Montreal, Bank of Canada, Export and Development Canada) <- Financial Mathematics and Economics Research hospitals (CHEO, Heart Research Institute) <- (Bio)statistics, Applied Mathematics CSIS <- Pure Mathematics DND (Department of National Defense)

7 Activity 1 How does GPS work? The story started in 1957 when the USSR launched the satellite Sputnik. The US military launched the first GPS in Major development started in Ronald Reagan declassified the GPS after the tragedy of Korean Air 007. Full operational capacity with 24 satellites was announced in The satellites orbit the Earth twice a day at an altitude km.

8 Activity 1 How does GPS work? You are lost at uottawa campus. You ask someone: Where I am? You are 200 m from the University Centre!

9 Activity 1 How does GPS work? You ask another person: Where I am? You are 150 m from the Math Department!

10 Activity 1 How does GPS work? You ask another person: How far am I from the main building? About 50m!

11 Activity 1 How does GPS work? This exercise should be accessible to grade 7 students. They practice the concept of radius, perimeter etc. Is this it? No, this is just a beginning!!! o The Earth is a sphere -> equation of a sphere; o Need for spherical coordinates; o A GPS receiver (your smart phone) sends a signal (that travels with a speed of light) to a satellite. The GPS measures the time that the signal travels from the receiver to the satellite and converts it into the distance ( distance = speed of light * time ) o. and then heavy math comes related to signal processing.

12 Activity 1 Where does it lead to? Telecommunication companies (wireless phone BlackBerry, France Telecom) DND Department of National Defense Source:

13 Activity 2 Cryptography Bob wants to send a secret message to Alice. They both know the key. For example, Digits Key Bob sends the message 34 which Alice easily can read as 23. Now, if someone else reads 34, how easy this person can decipher the code? There 10*9 possibilities to create a two-letter code with non-repeating digits. Using a computer the person can quickly break the code.

14 Activity 2 Cryptography This exercise teaches elements of combinatorics. Modern encryption keys are based on prime numbers factorization. Bob will send a number N which is a product of two prime numbers. The public can see only N. The public cannot see the prime numbers. Factorization is difficult. Breaking the code means finding these prime numbers. Exercise 1: Factorize into prime numbers 21=7*3 (easy). Exercise 2: Factorize into prime numbers 2178 (a little bit more difficult).

15 Activity 2 Where does it lead to? The next step is more serious mathematics that involves the modular addition, number theory, exponential functions and the Euler function. Employment opportunities: CSIS, IT companies etc. <- B.Sc. in Mathematics

16 Activity 3 Financial mathematics You take a loan $10,000. At the end of each year, you pay $2000. The annual interest rate is 10%. How long am I going to pay my loan? (certainly not 5 years!) o After year 1: You owe $10,000*1.1=$11,000; You pay $2,000. The balance left is $9,000. o After year 2: You owe $9,000*1.1=$9900; You pay $2,000. The balance left is $7,900. Until now you paid only $2,100 ($10,000-$7,900) of the principal and the reminder of $1,900 of interest!!! o.

17 Activity 3 Financial mathematics Can you come with a general formula using symbols: how much do you owe after the third, fourth etc. year? How much principal did you pay? One can add further complications: payments every month (so that the interest rate has to be divided by 12). Further complication: random interest rate. Each year you flip a coin: if HEAD, then the interest rate is 10%, if TAIL, the interest rate is 5%. This leads to different scenarios.

18 Activity 3 Where does it lead to? Employment opportunities in financial industry (TD Canada, Bank of Montreal, Bank of Canada, Export and Development Canada) <- B.Sc. in Financial Mathematics and Economics Sabrina Sixta (Joint Honours BSc in Financial Mathematics and Economics with GPA 10.0) Market Risk Analyst at BMO

19 Activity 4 Statistics Divide your class into 3 groups. Ask the first group: Do you like the school? Repeat the same for all groups. Here are hypothetical results: Group # of students Like Don t like % of likes % % % In the whole class (the population) 50% students like the school. The table above illustrates the sampling variability between different samples.

20 Activity 4 Statistics Groups 2 and 3 are not representative! If you ask 1000 Canadians Do you like Donald Trump? and 500 say YES, does it mean that 50% of all Canadians like DT? Or, there is a sampling bias? Statistics if the science about how to infer results from a sample to a population. Enormous employment opportunities: Government agencies (Statistics Canada, Health Canada, Environment Canada); research hospitals and everywhere <- B.Sc. in Statistics

21 Activity 5 Data Science How does Netflix recommend its movies? Assume that 3 movies are available: Pirates of the Caribbean; Bridget Jones's Diary; icarly. A 15-years old girl logs into her account. Which movie should be recommended to her? To answer the question, we will use Decision Tree. Historical data:

22 Activity 5 Data Science Gender Age Movie F 15 icarly F 30 Bridget Jones s M 30 Pirates M 15 Pirates F 15 Bridget Jones s F 15 icarly M 30 Pirates What is more important: gender or age?

23 Activity 5 Data Science Gender Age Movie F 15 icarly F 30 Bridget Jones s M 30 Pirates M 15 Pirates F 15 Bridget Jones s F 15 icarly M 30 Pirates All Men watch Pirates of the Caribbean, regardless of age

24 Activity 5 Data Science Gender Age Movie F 15 icarly F 30 Bridget Jones s M 30 Pirates M 15 Pirates F 15 Bridget Jones s F 15 icarly M 30 Pirates The age is not a determining factor (variable) If a men logs in -> recommend the Pirates

25 Activity 5 Data Science Gender Age Movie F 15 icarly F 30 Bridget Jones s F 15 Bridget Jones s F 15 icarly If a woman logs in, what should we recommend? If 30 years old -> recommend Bridget Jones s. If she is 15 years old, there is 66% (2/3) that she will like icarly.

26 Activity 5 Data Science Male Female Pirates icarly Bridget Jones s

27 Activity 5 Where does it lead to? Different Machine Learning algorithms Google, Amazon, Netflix etc. Any institution that needs prediction, classification etc. (e.g. credit card fraud detection, self-driving cars). TD Canada Bank is opening a Data Science group in Ottawa Joint Honours in Mathematics and Computer Science

28 Outreach at uottawa Math Horizons (Joseph Khoury) Math Camp (Joseph Khoury) Holiday Lecture Series NEW: Video competition for high schools on What is math NEW: Regular visits at uottawa or at your school WORKING ON: Math Fair present a project on a particular topic like: How does GPS work?; Cryptography; etc.

29 Thank you! Please don t hesitate to contact us for further information! Rafal Kulik Professor and Chair Department of Mathematics and Statistics matchair@uottawa.ca Yves Bourgault Professor and Associate Chair, Undergraduate Department of Mathematics and Statistics matugrad@uottawa.ca