Discrete mathematics is applied in many areas including the physical, engineering, and increasingly, the social sciences. This online textbook, written by mathematics and information technology professors, is aimed at students of information technology, computer science, and applied mathematics. The focus is on applying discrete math techniques from the two broad component areas of discrete math, namely combinatorics or enumerative techniques, and graph theory.

Discrete Mathematics: An Open Introduction is a free, open source textbook appropriate for a first or second year undergraduate course for math majors, especially those who will go on to teach. The textbook has been developed while teaching the Discrete Mathematics course at the University of Northern Colorado. Primitive versions were used as the primary textbook for that course since Spring 2013, and have been used by other instructors as a free additional resource. Since then it has been used as the primary text for this course at UNC, as well as at other institutions.

Discrete Mathematics Reading List

MTH 231 ELEMENTS OF DISCRETE MATHEMATICS
Elementary logic and set theory, functions, direct proof techniques, contradiction and contraposition, mathematical induction and recursion, elementary combinatorics, basic graph theory, minimal spanning trees.

Course outcomes: Students who complete MTH 231 will be able to:
1. Apply basic set operations.
2. Negate compound and quantified statements and form contrapositives.
3. Construct a direct proof (from definitions) of simple statements.
4. Apply the principle of mathematical induction.
5. Construct indirect proofs by contraposition and contradiction.
6. Construct explanations for solutions to counting problems.
7. Utilize one or more algorithms for finding a shortest path or a minimal spanning tree in a
connected graph.

This task asks students to find a linear function that models something in the real world. After finding the equation of the linear relationship between the depth of the water and the distance across the channel, students have to verbalize the meaning of the slope and intercept of the line in the context of this situation.

Using circumference, this segment measures the total distant traveled by two carousel riders after the carousel has rotated 10 times.

In this lesson, the teacher will demonstrate how to use the Pythagorean Theorem to find distance between two points in the coordinate system. In the coordinate plane, the difference in the x- and y-values will determine the numbers to calculate the distance. This lesson will use online graphing tools as well as graph paper to plot the points. This lesson can also be used to show the relationship between the distance formula and the Pythagorean Theorem. This lesson results from the ALEX Resource Gap Project.

An interactive applet and associated web page that demonstrate how to find the perpendicular distance between a point and a line using trigonometry, given the coordinates of the point and the slope/intercept of the line. The applet has a line with sliders that adjust its slope and intercept, and a draggable point. As the line is altered or the point dragged, the distance is recalculated. The grid and coordinates can be turned on and off. The distance calculation can be turned off to permit class exercises and then turned back on the verify the answers. The applet can be printed as it appears on the screen to make handouts. The web page has a full description of the concept of the concepts, a worked example and has links to other pages relating to coordinate geometry. Applet can be enlarged to full screen size for use with a classroom projector. This resource is a component of the Math Open Reference Interactive Geometry textbook project at http://www.mathopenref.com.

This short video and interactive assessment activity is designed to teach fifth graders about distances between points on multiple routes (metric units).

This short video and interactive assessment activity is designed to teach fourth graders about distances between points on one route (metric units).

This short video and interactive assessment activity is designed to teach fifth graders about measurement: greater than or less than a yard?.

The purpose of this task is meant to reinforce students' understanding of rational numbers as points on the number line and to provide them with a visual way of understanding that the sum of a number and its additive inverse (usually called its "opposite") is zero.

This task asks students to find equivalent expressions by visualizing a familiar activity involving distance. The given solution shows some possible equivalent expressions, but there are many variations possible.

This short video and interactive assessment activity is designed to teach fifth graders about dividing decimals by multiples of 10.

This short video and interactive assessment activity is designed to give fifth graders an overview of decimal division.

This short video and interactive assessment activity is designed to teach third graders about dividing by 1 digit numbers with illustrations.

This short video and interactive assessment activity is designed to teach fourth graders about dividing 2 digits by 2 digits with a remainder.

This short video and interactive assessment activity is designed to teach fifth graders about dividing 2 digits by 2 digits with a remainder.

This short video and interactive assessment activity is designed to teach fourth graders about the relationship between dividend, divisor and quotient.

This short video and interactive assessment activity is designed to teach fourth graders about estimating the number needed using remainders.

This short video and interactive assessment activity is designed to teach third graders about finding the remainder given the total number and number of groups.