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2017-07-13 13:31:57

Math Foundations for Career Success - GRE, GMAT, Interviews

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Learn Math to ace Competitive Examinations like the GRE/GMAT, and interview better for jobs

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- 9 hours on-demand video
- 66 Supplemental Resources
- Full lifetime access
- Access on mobile and TV

- Certificate of Completion

What Will I Learn?

- You will learn how to solve math problems at the harder levels of the GRE, GMAT, or SAT General Tests. You will also be able to demonstrate quant competence in (e.g. MBA or Engineering) job interviews.

Requirements

- There are no prerequisites for this course, but some familiarity with commonly tested concepts at the middle to high school level is assumed. We start with very simple math ideas and build from there.
- This course focuses on reviewing the important formulas and then demonstrating their application in solving problems of increasing difficulty. We solve some REAL interview questions.

Description

Busy professional studying to ace the GMAT and get that top MBA?

Forgot Math formulas but need to brush up quickly on basics for a Math Test?

Going to interviews, but need to quickly bone up on math for quant skills to succeed?

This course covers foundational mathematics with a view to helping you do better in competitive examinations like the GRE, the GMAT, or the SAT, as well as perform with confidence when quantitative questions are asked in job interviews. Useful for MBAs and Engineers alike, we cover all the material (our emphasis is on formulas and their application) from the very basics, and present and solve difficult problems in exercises to help you think critically and perform gracefully under pressure. Our focus is on building skill through practice solving harder and harder problems.

This course nicely supplements other resources you might already be using for test prep. While we do not teach python here, we do illustrate how you can use the computer to solve some small math problems - this format is becoming more prevalent in job interviews that have an online programming component.

We will move students from seeing the exam or interview as an obstacle in their path to success to viewing these as an opportunity to showcase their skills and talents to prospective employers to gain an edge over the competition.

If you aspire to improve your score or better your interview performance, this course will help you. Good luck!

A free ChiPrime book (with 100 solved problems) is included with this course. A Computer Adaptive Test interface is also provided on a best effort basis subject to capacity and bandwidth considerations. We intend to grow this course over time to make it still better taking in your feedback. Thank you.

Who is the target audience?

- Want that high percentile score in the GMAT, GRE, or SAT? Want to land that dream job or get admitted to the school of your dreams? This course may be for you.
- Anyone who wants to improve their core math skills can take this course. We target making students competent at math at the level of the GRE, GMAT or SAT, and for the quant aspects of job interviews at the MBA/beginner engineering level.

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Curriculum For This Course

72 Lectures

09:01:19
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Should you take this course?
3 Lectures
10:22

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Quick Formula Review & Sample Problems by Topic
35 Lectures
04:07:15

The solutions to each problem in the pre-course quiz are presented. Go through them now, but solving the quiz again once you finish the course, and going through the solutions again might also help.

pre-course quiz solutions

10:46

The first lessons are simple, yes. And feel free to skip these videos. But fret not, the questions that can be asked based on this content are not always easy. The Grab-bag questions will test your understanding, and if you conquer those, there are more waiting for you - just check the reddit link in the references, and try the problems on "properties of numbers".

Types of Numbers

05:57

The first lessons are simple, yes. And feel free to skip these videos. But the questions that can be asked based on this content are not always easy.

If p is a positive prime integer > 3, then (p^2 + 2^p) MUST be divisible by?

(a) 2

(b) 3

(c) 5

(d) 7

(e) None of the above.

The Properties of Integers - I

10:08

Already things start to get interesting, with GCD, LCM etc. - basic ideas and algorithms (e.g. Euclid) to deal with questions relating to the properties of numbers.

The LCM of A and B is twice their GCD. So:

(a) A=2B or A=B/2

(b) One of A or B must be odd

(c) A and B are both powers of 2

(d) None of the above may be True.

The Properties of Integers -II

06:20

Basic notions of fractions and numbers. Feel free to skip video if you remember how to work with these and you are able to easily complete the problem set.

A: The sum of the squares of a (positive) fraction X and its reciprocal.

B: The sum of fraction X and its reciprocal

Which is greater, A or B?

Operations with Integers, Fractions, and Decimals - I

07:01

Basic notions of fractions and numbers. Feel free to skip video if you remember how to work with these and you are able to easily complete the problem set.

The sum of the square of the fraction and the square of its reciprocal is 7, therefore the sum of the fraction and its reciprocal is?

Operations with Integers, Fractions, and Decimals - II

07:13

Ideas relating to roots and exponents presented here. Pay close attention, the problem set will test you.

If a^x = b^y, where "^" denotes exponentiation, then which of the following MUST be true?

(a) a=b

(b) x=y

(c) a=b and x=y

(d) none of the above need be true.

Exponents, Roots, and Logarithms - I

06:08

Logarithms. Again, the formulas seem easy and fun to recall.

If ln(x)=1/x, then x is: [given ln(2)=0.6931]

(a) < 1

(b) between 1 and 2

(c) between 2 and 3

(d) greater than 4

(e) none of the above.

Exponents, Roots, and Logarithms - II

04:59

This is where the rubber meets the road for the first time. You get to apply what you've learned so far to solve word problems relating mostly to work, ratios, interest, etc.

Actual interview question: 50,000 shoppers with a 0.5% conversion rate for a chair that costs $250. The company makes a 27% profit. Next, 50,000 shoppers will get a 10% discount. What is the conversion rate they must achieve to achieve the same profits as before?

Applications: Percentages, Ratios, Simple & Compound Interest

09:11

Progressions presented here. There is an optional lecture included in a later section on the finite differences method as it applies to series for those interested in learning more. Problems here can get hairy, so pay close attention.

1*2 + 2*3 + 3*4 + 4*5 +... to 10 terms =?

Arithmetic & Geometric Progressions

07:27

Looks simple, sounds simple, is simple.... but the applications and questions are not always easy (see the Grab-bag problems). There are optional lectures on standard deviation and the normal distribution in later sections for those interested.

Basic Statistics

06:09

Basic ideas of set theory. Feel free to skip if you already know all this.

Set Theory & Data Analysis - I

05:51

Set operations with an example. The ideas here are simple, but the questions you solve will show you simple doesn't always equate to easy. Some thinking needed.

Set Theory & Data Analysis - II

02:49

Basic linear equations and inequalities. Fun!

Linear Equations & Inequalities

05:33

We go through examples of simultaneous equations. Make sure you understand edge cases - when systems are solvable vs. not. We do **NOT** use matrix algebra - that is outside the scope of this course.

If the sum of two positive non-zero integers is equal to their product, their ratio is?

Simultaneous Equations

07:05

The formulas look like fun, and are... once you memorize them. Problems can also be a lot of fun, but the harder ones can sometimes be frustrating as well.

(x^2+24x-697)/(x-17) anyone?

Algebraic Expressions

09:25

Solving quadratic equations by factoring and applying the quadratic formulas. Not exactly rocket science.... or is it? (Newton's equation for distance travelled s = ut+1/2 at^2 looks like a quadratic in t - time, though we don't cover mechanics here).

Quadratic Equations - I

04:44

Vieta's formulas for quadratic equations - knowing these could save you time in examinations, and from embarrassment in interviews.

Quadratic Equations - II

06:41

How to get rid of the || in equations to solve them? One way of thinking through this.

Equations with Absolute Values - I

06:38

How to get rid of the || in equations to solve them? A second way of thinking through this. After finishing this module, please go back and look at the problem solved in the pre-course quiz. That is done using a third way with graphs - use whatever you're most comfortable with, or what applies most easily given the particular problem you are trying to solve.

Equations with Absolute Values - II

03:49

what are functions? how do they work? basic ideas. we do not cover notions of "injective", "bijective", "surjective" etc. our focus is on developing understanding to solve problems.

Functions - I

07:25

function inverses. since we do not cover trigonometry in this course, notions here are simple. however, the problems we see are not exactly trivial.

Functions - II

06:57

lecture discusses the basic formulas and how to apply them. we do not derive formulas - there are entire courses even at the graduate level on this topic, and people conduct research in combinatorics.

Permutations & Combinations (Combinatorics) -I

04:15

lecture discusses applications with a few examples. this is one of the more difficult areas tested in the GRE, the GMAT, the SAT and in interviews (yes, it is a favorite topic in interviews). you gain confidence through working more problems.

Real interview question: 5 people go out to dinner and end up sitting around a circular table. What is the probability they are sitting in the order of their ages?

Permutations & Combinations (Combinatorics) - II

07:52

we present the binomial theorem, how to compute coefficients, and Pascal's Triangle which comes in handy solving some challenging problems. later sections include an optional video on Bernoulli Trials and Binomial Experiments that leverages the content here to address some slightly more involved questions on probability

Binomial Theorem (Positive Integral Index)

08:21

this is **only** a quick overview of probability formulas. there are entire courses on probability - even at the graduate level (see references for details - the MIT OCW one and the Harvard one are particularly good) - we cannot do justice to the subject here in a ~10 min lecture other than go through basic notions.

Basic Probability Theory - I

08:58

simple examples that show how to apply the basic formulas. in the problem set and Grab-bag questions, we focus on how to solve problems in exams and in interview settings. interview problems can be difficult, but need to be solved in 3-5 mins. an optional video on Bayes' Theorem with solved examples follows in a later section.

Basic Probability Theory - II

08:58

basic ideas on lines and angles - quick refresher of concepts. safe to skip if you already know all this. lessons 18-20 have a single set of solved problems, since we need to build more "conceptual muscle" before we can test understanding.

Lines, Angles, & Triangles - I

07:33

triangles of different types, and basic properties thereof.

Lines, Angles, & Triangles - II

10:03

general right triangles and the application of the Pythagoras Theorem. too easy? then riddle me this: a right triangle with all integer sides has 17 as the measure of one side. the triangle's perimeter is?

Right Triangles & the Pythagoras Theorem - I

05:36

the 30-60-90 and 45-45-90 triangles, their properties, and simple examples - patience grasshopper, the harder ones show up in the problem sets, once you grasp the basics firmly.

a 30-60-90 triangle and a 45-45-90 triangle are drawn one on either side of their common hypotenuse of length s. the length of the other diagonal of the quadrilateral so formed is? (one diagonal is obviously the hypotenuse).

Right Triangles & the Pythagoras Theorem - II

07:36

simple ideas, but look at the Grab-bag for a couple of challenging questions. now we can solve problems for lectures 18-20 combined for all the concepts developed therein.

Quadrilaterals & Other Polygons

05:50

pay close attention, this topic is important. questions can get frustrating and drain your clock in an exam if you do not remember these formulas and how to apply them. lecture look too easy? the problem set will challenge you.

Plane Coordinate Geometry

08:48

basic properties of circles. arcs and their subtended angles are **not** covered. we can add this (of course with associated problems) if there is enough interest.

Circles

05:16

we go through the formulas and a couple of examples in the lecture and solved problems - covering cones, cubes, cuboids, spheres - nothing too crazy... yet. We have problem sets and the Grab-bag for that. :-)

Solids

09:53

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Problem Sets by Topic
15 Lectures
02:08:12

Enjoy the problem sets. Please try to read the solutions only after working through the problems. Please keep track of how long you take to solve the exercises, and what mistakes you make. And of course, please let us know if you see any errors here, or elsewhere on the course. No one is perfect, but with your help, we want to make the course as close to perfect as it can be. Thank you!

Preview
10:46

pset 2 - exponents, roots, logarithms

07:12

pset 3 - applications: ratios, interest, etc.

08:22

pset 4 - progressions and series

07:57

pset 5 - statistics and set theory

10:35

pset 6 - linear equations and inequalities

06:26

pset 7 - simultaneous equations

07:29

pset 8 - algebraic expressions and quadratic equations

06:26

pset 9 - functions

08:13

pset 10 - permutations and combinations

09:22

pset 11 - the binomial theorem

08:32

pset 12 - basic probability theory

11:17

pset 13 - plane coordinate geometry

10:50

pset 14 - lines, triangles, and circles

08:08

pset 15 - solids and mensuration

06:37

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Mega Grab-bag of Challenge Questions
5 Lectures
29:51

We hope these problems make you sweat at least a little. There are all 3 types of difficult ones here - those that mix different topics, those that are seemingly unapproachable with ideas you know, and those that press you to do more calculations to waste time. Try to finish all problems in 2 minutes or less - the easier ones should take no more than 20-30 seconds. Good luck!

Complete written solutions are provided for all problems. The video lecture here discusses only a selection of particularly challenging problems, how to think through them, and how to approach solving them in test- and interview- settings.

Challenge Questions 1-25 with Solutions

08:39

Complete written solutions are provided for all problems. The video lecture here discusses only a selection of particularly challenging problems, how to think through them, and how to approach solving them in test- and interview- settings.

Challenge Questions 26-50 with Solutions

07:00

Complete written solutions are provided for all problems. The video lecture here discusses only a selection of particularly challenging problems, how to think through them, and how to approach solving them in test- and interview- settings.

Challenge Questions 51-75 with Solutions

05:17

Enjoy these problem sets?! Please tell us what could be made more challenging, and what you found to be frustrating. If you want more:

- try the Computer Adaptive Tests. The references section will tell you how to get these FREE.
- also included for FREE with this course is a book with 100 solved problems - in the references section.

Challenge Questions 76-100 with Solutions

04:58

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Performance Excellence in Competitive Examinations & Interviews
2 Lectures
17:16

Suggestions on strategy and tactics to maximize your score.

Test-taking Strategies & Tips

07:33

What can you do in interviews to be the best that you can be? Also, please see additional FREE resources like question sets for different kinds of interviews, in the references section.

Interview Strategies & Tips

09:43

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Quick Overview of Programming Problems for Interviews
2 Lectures
18:09

A whirlwind tour of the Python programming language - not a full-fledged course, but enough to whet your appetite and hopefully make you want to learn more. Later sections use this language to introduce some ideas for interviews and application on the job. Worthwhile learning. Strongly recommended.

Foundational Ideas for Programming (Python 2.x)

12:01

These were collected from real interviews and are offered without solution. Yes, you can use HackerRank, LeetCode, CareerCup and the like to get more.

Sample First Round Programming Problems

06:08

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Miscellaneous Additional Material
8 Lectures
01:14:09

These are sometimes tested in examinations, can be derived when needed, but lecture is a quick refresher so will save time if you memorize the formulas.

Circles of Triangles (in-circles, circum-circles)

06:54

powerful technique with an application to illustrate its use in series and progression problems.

Method of Finite Differences

08:47

worthwhile studying. this lecture covers the basic idea of dispersion and its measure, and shows you how to perform simple computations using a spreadsheet. (no, we don't teach Excel in this course, but you need basic spreadsheet skills in almost every job today).

Standard deviation - a measure of dispersion

11:25

useful to know, and sometimes tested in competitive examinations. sure, you can solve these problems from first principles, but knowing formulas and how to apply them can only save you time.

Bernoulli Trials and Binomial Experiments (Probability)

08:49

useful, important, and an **overwhelming favorite** when it comes to probability questions asked in interviews in high-technology and financial services firms. we solve a real interview question here.

Bayes Theorem

08:52

this lecture builds on earlier lectures to scrape the surface on how simulations can be used to solve difficult real world problems on the job. a complete course on simulation it is not, but packs a powerful punch in just over 9 minutes. uses python to illustrate ideas.

(Monte-Carlo) Simulation

09:20

A: am I normal?

B: what's your kurtosis?

The normal distribution is widely used, we cover only the simplest ideas relating to this. And oh, if A has kurtosis significantly different from 3, s/he probably isn't (normal that is).

Normal Distribution

11:28

modular arithmetic is sometimes useful to solve difficult problems relating to the properties of integers. in this lecture, we study this technique, and solve a couple of examples using it to ground our understanding.

Preview
08:34

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Additional Resources & References for Further Study
2 Lectures
16:05

We cover a **LOT** of ground in this course, __ but we cannot cover everything__. This section has resources you can explore on your own to do more. We'd love to hear your feedback and your success stories though, so please do write us. Also, if you'd like to see other topics covered, let us know, and we may, if there is sufficient strong interest.

Also, keep watching, __more questions may come your way in this course!__

Good luck with your examinations and your interviews! At ChiPrime, we bask in your glory.

[Bonus Lecture] References

09:59

Applying to and getting accepted into a top-tier MBA program is stressful. Here's some quick advice for MBA aspirants from someone who's been there.

For MBA Aspirants

06:06

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