Link to Homework 7, due Monday April 13

Click on this link.

If you want to follow along with today's lecture, click here.

Link to April 6 lecture on YouTube

https://www.youtube.com/watch?v=l2RuhHv4AYI

UPDATE: Classes begin on Zoom on Monday, April 6 at 9:30

You can access Zoom on a laptop or on a cellphone. The number for the class at 9:30 is

635-591-163

The number for the 12:20 office hour is

584-656-357

Hope to see you all this Monday. 

Below is a link to my class notes for this week.

https://drive.google.com/file/d/16-F4fKvYJjHOP6HueN-9GPfDC_J0HTCT/view?usp=sharing

Face to Face classes are canceled until Wednesday, April 8

No instruction, not face to face or online, will take place for the rest of the month.

Stay Safe,
Prof. Hubbard

Face to face classes are canceled on Wednesday, March 11

Laney has canceled face-to-face classes from Wednesday, March 11 to Saturday, March 14.

If you are enrolled in Math 15 and you read this, please send me an email at mhubbard@peralta.edu and include your student ID number.
 

The biographies of six computer scientists

Short biographies of John Von Neumann, Alan Turing, Grace Hopper, Edsger Dijkstra and Donald Knuth

NASA's page about Katherine Johnson
 

Notes for Homework 5

Notes on Richter scale and the bel/decibel system

Notes on set theory and Venn Diagrams
 

Notes for Homework 4

Defining a triangle by three side lengths

Defining a triangle by three points in the plane
 

Notes for homework #3

Scientific notation

Approximating and simplifying square roots

Classifying triangles defined by three angles

Finding isosceles triangles
 

Notes for Homework #2

Notes for time conversion

Notes for converting between binary, decimal and hexadecimal

Notes on the logical operators AND (^), OR (v) and NOT (~)

Notes for Homework #1

Time addition and subtraction problems

Notes for fractions, decimals, and percents, prime factorization and finding all factors

Link to the biographies of five British logicians

Link to the biographies

Notes for Homework 11, due Mon., 11/18 (not accepted late)

Notes on statistics: mean, median and mode

Notes on the five number summary and the IQR method for finding high and low outliers

Notes for Homework 10, due Wednesday Nov. 13 (Monday is a holiday)

Notes on Roman numerals and Hindu-Arabic numerals

Notes on repeating fractions and decimal representations

Fractions, percent and decimals

Notes for Homework 9, due Nov. 4

Notes on interest rates on money put in the bank.

Notes on the Consumer Price Index table.

Notes on paying back loans.
 

Notes for Homework 8, due Mon., Oct. 21

Notes for conversion from metric to customary and vice versa

Changing Celsius to Fahrenheit

F = 9/5 C + 32

Changing Fahrenheit to Celsius

C = 5/9(F - 32)

Notes for Homework 7, due Oct. 7

Notes on coin problems (simultaneous equations)

Notes on slope, the point-slope formula and the slope-intercept formula 

Notes for Homework 6 due Sept. 30

Notes on contingency tables

Notes on interior angle sums and regular angle measures

Notes on death rates and the scale per 100,000 people

Notes on Set Theory
 

Notes for Homework 5, due September 23

Notes on the Richter scale and the bel/decibel system for measuring sound

Notes on Venn diagrams

We will have three sets.

U is the universe, all the things that we will discuss.

A and B are the subsets.

The universe is the rectangle, A and B are the two ovals. A on the left and B on the right.

Example. Let the universe be U = {a, b, c, d, e, f, g}

A = {b, e, a, d}
B = {f, a, c, e}

a and e are in the middle sliver, while b and d are in the left oval and f and c are in the right oval.  The letter g isn't in either list, so it goes outside the circles.

Sorry the picture is hard to read.

Notes for Homework 4, due Mon., Sept. 16

Notes on Heron's formula with practice.

Notes on classifying triangles defined by three side lengths, with practice problems.

Notes on triangles defined by three points in the plane.

Notes for homework 3, due Monday, Sept. 9

Notes on square roots, approximate values and simplified forms

Notes on classifying triangles defined by three angles 
 
Notes on creating isosceles triangles given one or two of the three angles

Notes for Homework 2, due Wed. Sept. 4 (Monday is a holiday)

Notes for conversion from hexadecimal to binary and vice versa, also binary to decimal and vice versa

Notes on logical operators AND (^), OR (v), NOT (~)

Notes on scientific notation

Notes for Homework 1, due Monday, August 26

A link to the methods for changing between decimal, binary and hexadecimal number systems
 

A link to the stories of six computer scientists

Click here to read the stories of Von Neumann, Turing, Hopper, Dijkstra and Knuth

Click here for the NASA page on Katharine Johnson

Notes for Homework 10, due Mon. April 29 NOT ACCEPTED LATE

Notes on converting from metric to customary and vice versa

Changing Celsius to Fahrenheit

F = 9/5 C + 32

Changing Fahrenheit to Celsius

C = 5/9(F - 32)

 

Notes for Homework #9, due Mon., Apr. 22

Notes on loans and investing and the Consumer Price Index
 

Notes for Homework #8, due Monday, April 15

Notes on mean, median and mode


Notes on the five number summary, IQR and the high and low outlier thresholds

Notes on z-scores and percentages, using the look-up table
 

Notes for Homework 7, due Wed. March 27

Notes on contingency tables

Notes on currency problems, either coins or bills

Notes on slope, point-slope and slope-intercept

Notes for Homework 6, due Tues. March 19

Notes on death statistics and scales dealing with powers of ten. 

Notes on interior angle sums and the regular angle measure for polygons with n sides.

Notes on set theory.

Notes on Venn Diagrams.

A link to notes on four famous mathematicians

Click on this link to read about Archimedes, Newton, Euler and Gauss.
 

Notes for homework #5, due Wednesday, Feb. 27

Notes on the triangle inequality, classifying triangles defined by side lengths and Heron's formula

Notes on triangles defined by three points in the plane, where one point is (0, 0)

Notes for Homework #4, due Feb. 20

Notes for bels and decibels, comparing the energy in sounds and calculating the decibel reading for a group of instruments. Notes for the Richter scale comparisons.

Note for triangles defined by three angles

Notes for Homework #3, due Feb. 11

Notes for scientific notation

Notes for simplifying and approximating square roots
 

Notes for Homework #2, due Mon., Feb. 4

Notes for rounding to a position

Notes for rounding to a given number of significant digits

Notes for changing between decimal, binary and hexadecimal

Notes for the logical operators AND (^), OR (V) and NOT(~)

Notes for Homework #1, due Jan. 28

Notes for percent to decimal to fraction in lowest terms

Notes for reducing fractions

Notes for repeating decimals

Notes for rounding decimals

Notes for prime factorization and all factors of a number

Notes for adding and subtracting time
 

Notes for Homeworks 11 and 12

Notes for converting Celsius to Fahrenheit and vice versa

Notes for converting metric to customary and vice versa

 Changing a repeating decimal representation to a fraction in lowest terms

Roman numerals to Hindu-Arabic and vice versa
 

Notes for five British logicians

Notes on the lives of George Boole, Charles Dodgson, Charles Babbage, Countess Ada Lovelace and Augustus de Morgan

Notes for Homework 10

Notes for interest, CPI and inflation rates, and paying back loans

Notes for Homework 9

Notes for average (mean), median, mode, the five number summary, IQR and the simplest definition of an outlier

Notes for z-scores and the look-up tables associated with normally distributed sets


 

Notes for Homework 8

Notes for slope, the point-slope formula and the slope-intercept formula

Notes for coin problems
 
Notes for contingency tables and probabilities taken from contingency tables

Biographies of 20th Century computer scientists

A link to the stories of Von Neumann, Turing, Hopper, Dijkstra and Knuth

A link to a NASA webpage about Katherine Johnson
 

Notes for Homework 7

Notes on set theory and Venn diagrams

Notes on scales based on powers of 10 smaller than percent, like death rates counted per 100,000 population
 

Notes for Homework 6

Notes about triangles defined by three vertices

Notes about polygon interior angles sums and the regular angle for an n-sided polygon

Notes for Homework 5

Notes for classifying triangles by angles or by side lengths

Practice problems for the triangle inequality and Heron's Formula

 

Notes for Homework 4

Notes on bels/decibels and the Richter scale, two logarithmic scales

Notes on simplifying and approximating square roots

Notes for Homework 3

Notes for time given in decimal form

On Earth, a years is actually 365.2422 days. We make up the extra number by having a leap year every four years, with a few exceptions. How long is 0.2422 days in hours minutes and seconds?

Decimal days to hours, minutes and seconds:  To get the number of hours, we multiply 0.2422x24 = 5.8128 hours, we save the 5, then multiply the 0.8128 x 60 = 48.768, which means we now have 365 days, 5 hours, 48 minutes and some decimal part of a minute. 0.768x60 = 46.08 seconds, which means a year is 365 days, 5 hours, 48 minutes and 46.08 seconds.


A day on Saturn is 10.656 Earth hours. How do we change the decimal to hours, minutes and seconds?

Decimal hours to minutes and seconds: Multiply the decimal part by 60. In this case, .656 x 60 = 39.36 minutes. We save the 39 minutes and then multiply .36 x 60 = 21.6. This means the final answer is 10 hours, 39 minutes, 21.6 seconds.

Notes for scientific notation

Notes for Homework 2

Notes for rounding to positions and rounding to significant digits

Notes for rounding error

Notes for changing between decimal, binary and hexadecimal

Notes for the logical operators AND (^), OR (v) and NOT (~)

Notes for Homework 1

Notes for percent, decimal and fractions and notes for factorization

 Notes for adding and subtracting time
 

Links to the stories of Archimedes, Newton, Euler and Gauss

Click on this link to read the stories of four great mathematicians. The first quiz on Wednesday, August 22, will be fill in the blank.
 

Notes for Homework 12, due May 8

Notes for Roman numeral to Hindu-Arabic numeral conversion

Notes for repeating decimals to fractions

Notes for percent, decimals and fractions over 100
 

Notes for Homework 11a, due May 1

Notes on the metric system vs. customary

Changing Celsius to Fahrenheit

F = 9/5 C + 32

Changing Fahrenheit to Celsius

C = 5/9(F - 32)

Link to biographies of five British logicians

Link to the biographies of Babbage, Boole, de Morgan, Dodgson and Lovelace

Notes for Homework 10, due April 17

Notes for interest rates on investment, the Consumer Price Index and paying back loans
 

Notes for Homework 9, due April 10

Notes on mean, median and mode

Notes on the five number summary and outliers

Notes on z-scores, normal distribution and proportions

Notes for Homework 8, due March 28

Notes on determinants

A 2x2 matrix is an array of four numbers put in two rows and two columns, such as

| a c |
| b d |

The determinant of this matrix is ad - bc, the product of the main diagonal minus the product of the opposite diagonal. If you use Kramer's rule to solve a pair of simultaneous equations, you will need to know how to calculate determinants.

For example, let's consider the following set of equations.

3x - 2y = 7
2x + 4y = 12

As an augmented matrix , these equations become

|  3  -2  : 7 |
|  2   4  : 12|

Matrix_1 is

| 3 -2 |
| 2  4 |

The determinant is 3(4) - 2(-2) = 12 - -4 = 16
 

Matrix_x is

| 7 -2 |
| 12  4 |

The determinant is 7(4) - 12(-2) = 28 - -24 = 52
  Matrix_y is

| 3  7  |
| 2 12 |

The determinant is 3(12) - 2(7) = 36 - 14 = 22

From here, Kramer's rule then has x = 52/16 = 13/4 or 3 1/4. The value for y = 22/16 = 11/8 = 1 3/8
 
  Notes on solving simultaneous equations
 

Notes for Homework 7, due March 20

Notes for contingency tables

Notes for coin problems

Notes for slope, point-slope and slope-intercept
 

Notes for Homework 6, due March 13

Notes on rates other than percent

Notes on set theory and Venn diagrams
 

Link to biographies of Archimedes, Newton, Euler and Gauss.

Link to the biographies

Notes for Homework 5, due Feb. 27

Notes on area for a triangle defined by three points

Notes on the distance formula

Notes on interior angles of polygons and regular angles
 

Notes for Homework 4, due Feb. 20

Notes for classifying triangles by angles and by side lengths

Notes on creating isosceles triangles


Notes on Heron's Formula (lots of practice with answers in the comments)
 

Notes for Homework 3, Due Feb. 13

Notes on Richter scale and bels/decibels


Notes on simplifying and approximating square roots

Notes for Homework 2, due Feb. 5

Notes on adding and subtracting time, and notes on converting time

Notes on scientific notation
 

Notes for Homework 1, due Tues., Jan 30

Notes on rounding

Notes on binary, decimal and hexidecimal

Notes on the logical operators
 

Notes for Homework 13, due, Mon., Dec 4

Notes on Roman numerals

Notes on repeating decimals to fractions and vice versa

Notes on decimals, fractions and percents
 

Notes for Homework 12, due Mon., Nov 27

Notes on the metric system

Changing Celsius to Fahrenheit

F = 9/5 C + 32

Changing Fahrenheit to Celsius

C = 5/9(F - 32)




 

Notes for Homework 11, due Nov. 13

Notes for CPI table, interest on savings, effective interest rate and interest on loans
 

Notes for Homework 10, due Mon. Nov. 6

Notes on mean, median and mode

Notes on the five number summary, IQR and the calculation of low and high outlier thresholds

Notes on z-scores and table lookup
 

Notes for Homework 9, due Monday, Oct. 30

Notes on simultaneous equations and Kramer's Rule

Notes for Homework 8, due Oct. 23

Notes for contingency tables

Notes for coin problems

Notes for slope, point-slope and slope-intercept 

Notes for Homework 7, due Mon., Oct 16

Notes on set theory and Venn diagrams

Notes on rates based on powers of ten, most often on the per 100,000 scale

History lesson for Wednesday quiz

Here is a link to the biographies of Von Neumann, Turing, Hopper, Dijkstra and Knuth.

Here is a link to NASA's page on Katherine Johnson.

Notes for Homework 6, due Monday Oct. 2 (not accepted late)

Notes for triangles defined by three points: area and classification

Notes for interior angle sum and regular angle formula fro a polygon with n sides

Notes for Homework 5, due Sept. 25

Classifying Triangles by the three angles -or- by the three side lengths


Finding the area of a triangle using Heron's Formula

Notes for Homework 4, due Sept. 18

Practice for bels and decibels, also the Richter scale

More on the Richter scale

Simplifying and approximating square roots

Notes for Homework 3, due MONDAY, SEPT. 11

Notes for decimal part of a day to hours, minutes and seconds.

Notes for scientific notation

Fractional part of a day

A year is defined by how long it takes a planet to make a single orbit around the sun. An Earth year is 365.2422 days. To make up for the decimal part we have a leap year every four years and skip the leap year if the number of the year is divisible by 100. This means we had leap years in 2004, 2008, 2012 and 2016, but we did not have one in 2000. What this lesson is about is to take the decimal part of this time and turn it onto hours, minutes and seconds.

Step 1. Multiply the decimal part by 24 to get the number of hours.
In this case, .2422 x 24 = 5.8128, which means 5.8128 hours.

Step 2. If there is still a decimal part, multiply it by 60 to get the number of minutes. We know know a year is 365 days, 5 hours and some number of minutes. That number is 60 x .8128 = 48.768

Step 3. If there is still a decimal part, multiply it by 60 to get the number of seconds.
We know know a year is 365 days, 5 hours, 48 minutes and some number of seconds. That number is 60 x .768 = 46.08. In these problems, it is okay to round to the nearest tenth of a second, so the final answer is 365 days, 5 hours, 48 minutes and 46.1 seconds.

Let's do another example. A year on Venus is 224.65 Earth days.

Step 1. .65 x 60 = 15.6, so the year on Venus is 224 days, 15.6 hours.

Step 2. 60 x .6 = 36, so that makes the year on Venus 224 days, 15 hours and 36 minutes. There is no more decimal part, so we don't have to add any seconds to our answer.

Here are two more practice problems. The answers are in the comments.

1. It takes Mercury 87.969 Earth days to travel around the sun. Write this number in days, hours, minutes and seconds.

2. It takes Mars 686.98 Earth days to travel around the sun. Write this number in days, hours, minutes and seconds.

Notes for Homework 2, due WEDNESDAY, SEPT. 6

Notes on hexadecimal, binary and decimal

Notes on logic with 1s and 0s

Notes on time problems

Notes for Homework 1, due August 28

Notes on rounding

Notes on significant digits

Notes on binary to decimal and vice versa

Link to the biographies of Archimedes, Newton, Euler and Gauss

Click on this link to read a post on the four great mathematicians listed above

Notes for Homework 9, due Monday, July 24

Notes on the five number summary method for determining outliers

Notes on z-scores and normal distribution
 

Notes for Homework 8, duy Wed. July 19

A quick reminder: this homework will not be accepted late because the answer sheet will be given out at the end of class to help study for Thursday's midterm.

Notes on scientific notation

Notes on Set Theory

Notes on Venn Diagrams

Notes on contingency tables and probabilities

Math history: Five Briitsh logicians

 Here is a link to stories about Boole, Babbage, Dodgson, de Morgan and Countess Lovelace

Notes for Homework 7 due Monday, July 17

Notes on simultaneous equations

Notes on using elimination in coin problems

Notes for Homework 6, due Wednesday July 12

Practice problems for distance.

Practice problems for slope, point-slope and slope intercept.

Notes for Homework 5, due Tuesday July 11

Notes for classifying triangles by angles or by side lengths

Note for finding area using Heron's formula
 
 

Link to the history of five computer scientists

A link to the biographies of Von Neumann, Turing, Hopper, Dijkstra and Knuth.

Notes for Homework 4, due Monday July 3

Notes on decibels and bels (measuring sound) and the Richter scale (measuring earthquakes)

Notes on square roots, approximate and simplified, also Pythagorean Theorem problems

Notes on rates at different scales, notably death rates per 100,000 people

 

Notes for Homework 3, due June 28

Notes on interest rates on investments, interest rates on loans and the Consumer Price Index

Notes on rounding to significant digits
 

Notes for Homework 2, due June 26

Notes for converting from binary (base 2) to decimal (base 10) and binary to hexadecimal (base 16)

Notes for the logical operators AND (^), OR (v) and NOT (~)

Converting repeating decimals to fractions in lowest terms

Time problems

Roman numerals

Notes for Homework 1, due June 21

Notes on fractions, decimals and percents, also on primes and prime factorizations.

Notes on repeating decimals and rounding decimals.

Notes on adding and subtracting time.
 

Link to the stories of four famous mathematicians

The biographical data on Archimedes, Newton, Euler and Gauss.

Notes for Homework 7, due March 27

Contingency tables and probabilities

Two points: Find slope, then the point-slope, then slope-intercept

Coin problems
 

Notes for Homework 6, due March 20

Notes on Set Theory and Venn Diagrams

Notes on interior angle sums and regular angles

Notes on tilings of the plane

Notes on the area of a triangle given three points on the plane
 

Link to the biographies of five computer scientists

Link to the biographies of John Von Neumann, Alan Turing, Grace Hopper, Edsger Dijkstra and Donald Knuth.

Notes for Homework 5, due Monday March 6

Note for classification of triangles by angle measurement and side length

Area by Heron's formula
 

Notes for Homework 4, due Wed. Feb. 22

Because of the Monday holiday, homework is due on Wednesday. There will be no quiz this week.

Notes on the Richter scale and bels and decibels, abbreviated B and dB.

Notes on square roots and the Pythagorean Theorem.

Notes for Homework 3, due Monday, Feb. 13

Practice with decimals and percents

Practice with scales of powers of ten other than percent

Practice with scientific notation
 

Notes for Homework 2, due Monday, Feb. 6

Notes on Hex to Binary and vice versa.

Notes on logical operators AND (^), OR (v) and NOT (~).

Notes on time conversion and adding and subtracting time.

Notes for Homework 1, due Monday, January 31

Links to posts on rounding.

Links to posts on significant digits.
 
Links to posts on decimal to binary and binary to decimal.
 

Link to the biographies of Archimedes, Newton, Euler and Gauss

Click on this link to a post that has the biographies of the four guys I discussed Monday night, the information that will be on the quiz on Wednesday.