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Sharon K. Robbert, Professor of Mathematics
Christianity and Mathematics
Devotionals connected to mathematical contentSingle-variable Calculus | Multivariable Calculus | Discrete Structures
Linear Algebra | Differential Equations | Statistics
Discrete Structures
Devotional Title Course Topic Scripture References Proof of God's Will Overview: Conjecture and Proof Romans 12:1-2 Epistle Implications Logical Operators 1 John 1:5-9 Unique Existence of God Logical quantifiers Exod 3:13-14, Deut 6:4-5, Rom 1:18-20 A Perfect Proof? Proof writing James 2:8-11 Recursive Blessings and Curses Recursion and Induction Exodus 20:4-6 Adopted Children of God Disjoint Sets Eph 1:3-9 The Jesus Function Definition of Function Isaiah 1:18 Christ = Adam-1 Inverse Functions 1 Corin 15:20-23 A Common Confession Equivalence Classes Rom 10:9-10, Phil. 2:9-11 Countable or Uncountable? Combinatorics Numbers 1:46, 1 Chron 21:1-14, Neh. 11:1-20, Luke 2:1-3, Rev. 7:4, 9
Proof of God's WillRomans 12:1-2back to topOne thing that developing mathematicians must learn to do is to design new mathematical systems. At the sophomore level, we begin that process within a system where students have a lot of experience---number relationships. Students look at simple patterns and try to generalize the relationships they see. The generalization created is called a conjecture. Conjectures are excellent first steps in the design of new mathematical systems; however, to be useful, the person must try to write a convincing argument demonstrating why the statement is true or find a counter-example demonstrating why the statement is false.
Developing Christians are taught to seek the will of God in making life-decisions. To be able to determine the direction God wishes us to go, we must form conjectures and reason to conviction of truth. Paul says in Romans 12:2, "be transformed by renewing of your mind. Then you will be able to test [conjecture] and approve [reason to conviction of truth] what God's will is ."
Epistle Implications1 John 1:5-9back to topThere are lots of logical implications in the new testament. Read any letter written by Paul, for example, and look for the word "therefore." An important pair of implications is found in 1 John 1:
vs. 8: If we say we are without sin, [then] we deceive ourselves and the truth is not in us.Note in particular that the verse 9 implication uses the negation of the hypothesis of verse 8 as its premise. It is also interesting that the conclusion of verse 9 shifts emphasis from man to God. These two verses cover all cases in an analysis of how man responds to his relationship to sin: either you deny your sin or you confess your sin.
vs. 9: If we confess our sins, [then] he is faithful and just and will forgive us our sins and purify us from all unrighteousness.
Unique Existence of GodExod 3:13-14, Deut 6:4-5, Rom 1:18-20back to topIn the process of learning acceptable mathematical procedures for writing an argument which is convincing to other readers, we study predicate logic. Determining what portion of the entire collection will satisfy a relationship is one component of the argument. Mathematicians indicate the special cases of all, at least one, and exactly one with quantifier notation. If an open statement P(x) is true for all valid replacements x, we write "x,P(x). If the open statement P(x) is true for at least one replacement, we write $x,P(x). And, if an open statement is true for one and only one replacement, we write $!x,P(x). Unique existence of a valid replacement is one of the most special cases to consider. A proof of this type of statement always requires two parts: first, you must show that at least one solution exists (i.e., existence of solution); then you must show that not more than one solution exists (i.e., uniqueness of solution).
Abraham and his descendants were chosen to be the first people on earth to be led to comprehend both aspects of the unique existence of God. One instance of the existence portion of God is found in the story of Moses meeting God in the burning bush. Here, God reveals his name to Moses as evidence that He truly exists. God says, "I am who I am." [Note: Exodus 3:13--14. I especially enjoy the transcendence of God to time given within the Hebrew for this phrase--the phrase can be interpreted with past, present, and future verb tenses!]
Later, at Mount Sinai, Moses is given laws to train the infant-nation of Israel in the ways of God. In Deuteronomy 6:4, Moses recounts the uniqueness condition told him by God: "Hear, O Israel: The Lord our God, the Lord is one." Even though both aspects of the "$! God" were provided to Israel from the time of the exodus, we know from Old Testament stories that the lesson was a difficult one for these chosen people to learn. I think even today we struggle with acknowledging God's unique existence, though few Christians will deny the truth of the statement.
A Perfect Proof?James 2:8-11back to topSuppose you write a proof that is perfect--except at one point where there is a logical flaw. Does the proof hold? Of course the answer is "no." The proof must have absolutely no logical flaws to be accepted as valid. The same is true of people who try to keep the law of God perfectly. If there is even one small part that is not held perfectly, the entire law is broken. Since we cannot keep the law perfectly, our judgment is death apart from Christ.
Recursive Blessings and CursesExodus 20:4-6back to topRecursion and Induction are important topics in mathematics and computer science. In each context, one takes a initial object (a base case or cases) and creates new objects from ones already known with a recursion. For example, to define n! using a recursive definition, one defines 0! to be 1 and says that (n + 1)! = (n + 1) × n!. Or, to prove that a statement is true for all natural numbers using math induction, one first proves that the statement is true for the case n = 1, then one proves that IF the case with n = k forces the case with n = k + 1 to also be true regardless of the k-value selected, then the statement must be valid for all natural numbers.
It is interesting to note that God also uses the concept of recursion. In the third commandment, do not worship idols, God makes it very clear that he will punish or reward people based on their response to this command. God will recursively punish children for three to four generations for the sin of one person. But His recursive blessings for those who love Him and keep his commandments will go to thousands!
Adopted Children of GodEph 1:3-9The Jesus FunctionTwo sets are disjoint if they have no elements in common. In this case, we write A ÇB = Æ. Disjoint sets of objects are easy to create; consider, for example, the sets A = {1, 3, 5} and B = {2, 4}. These sets have no numbers in common.
Okay, so what about people? Are there disjoint sets of people? Many would like to claim that we are separated by race or creed or nationality. But through Christ we know that in God's eyes these are not true distinctions (see Gal 3:28). God does separate people into a pair of disjoint sets (which is actually a partition): people who are redeemed and people who are not redeemed. Those who are redeemed are adopted heirs of salvation through faith in Jesus. However, people are not given the insight to determine who is in each of these sets. It is the commission of redeemed people to spread the good news of salvation to all people and let God sort out who will be in each set.
Isaiah 1:18back to topA functions is a rule which assigns to each object in a domain set exactly one object in a codomain set. So, suppose that the domain set is the collection of behaviors that people do and the codomain consists of two values: perfect or imperfect. On our own, every behavior that we do is mapped to the "imperfect" output value. But, the Jesus function takes our behavior and filters it through his sacrifice so that God takes the output of the behavior of Christians as "perfect" in terms of our final judgment. Praise God!
Christ = Adam-11 Corin 15:20-23back to topAn inverse mapping of any function reverses the direction of the assignment of the function. In the case that the original function is one-to-one, the inverse mapping will also be a function with the domain and codomain interchanged.
Through the sin of Adam, all people are condemned for eternity. We cannot escape our inherited imperfection. Let's define the "Adam life function" to act on people. This function has output death for all inputs. However, Christ inverts the total condemnation of people through his death and resurrection. This acts as a sort of inverse to the "Adam life function;" the "Christ death function" acts on all people and brings life to those who believe. This is not truly an inverse function--it is more of a negation--the negation of Adam (man) is Christ and the negation of life is death. It is ironic that to give eternal life to people whose lives are undeserving, Christ had to die.
A Common ConfessionRom 10:9-10, Phil. 2:9-11back to topA partition of sets is a separation of every element from a universal set into a collection of pairwise disjoint sets. If a valid partition is created, then one can create from that partition an equivalence relation on the universal set. Two objects will be equivalence if they fall in the same subset of the partition. God has partitioned people into two sets: the redeemed and the unredeemed. But, regardless of classification, ALL will someday confess that Jesus is Lord.
Countable or Uncountable?Numbers 1:46, 1 Chron 21:1-14, Neh. 11:1-20, Luke 2:1-3, Rev. 7:4, 9back to topThere are numerous events where counting occurs in the Bible. The resulting numbers recorded are not necessarily literal, though. Many of the results are figurative. Some of the counting events were performed at God's command while other counts were due to the pride men. For example, we read that there are roughly 600 thousand Israelite men at the time of the exodus from Egypt. Later the number of "fighting men" in Israel was counted to be 1.1 million by David the King in a moment of doubt, and then 70 thousand of these men were killed in a plague of judgment. After the exile, 10% of the remnant were chosen to live in Jerusalem. These men numbered 3,044 "brave men." So, the remnant of Israel number in all approximately 30 thousand men. Rome took a census at the time of Jesus birth--though the results are not recorded in scripture. In the vision of John recorded in Revelations, 144 thousand people from the tribes of Israel were given a seal on their foreheads but an uncountable number in white robes from "every nation, tribe, people and language" before the throne of the Lamb!
Project Overview
Devotionals connected to mathematical contentSingle-variable Calculus | Multivariable Calculus | Discrete Structures
Linear Algebra | Differential Equations | Statistics
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skr--Spring 2003Mathematics | Sharon Robbert | Triathlon | Christianity & Mathematics | Vita