INTRODUCING PROOF TECHNIQUES USING THE LOGICAL GAMEMINE HUNTER

Allan Alexander Struthers

doi:10.1080/10511979508965778

PARITY RESULTS FOR PARTITIONS WHEREIN EACH PART APPEARS AN ODD NUMBER OF TIMES

Bulletin of the Australian Mathematical Society ◽

10.1017/s0004972718001041 ◽

2018 ◽

Vol 99 (1) ◽

pp. 51-55

Author(s):

MICHAEL D. HIRSCHHORN ◽

JAMES A. SELLERS

Keyword(s):

Generating Function ◽

Proof Techniques ◽

One To One

We consider the function $f(n)$ that enumerates partitions of weight $n$ wherein each part appears an odd number of times. Chern [‘Unlimited parity alternating partitions’, Quaest. Math. (to appear)] noted that such partitions can be placed in one-to-one correspondence with the partitions of $n$ which he calls unlimited parity alternating partitions with smallest part odd. Our goal is to study the parity of $f(n)$ in detail. In particular, we prove a characterisation of $f(2n)$ modulo 2 which implies that there are infinitely many Ramanujan-like congruences modulo 2 satisfied by the function $f.$ The proof techniques are elementary and involve classical generating function dissection tools.

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Proof Techniques

Proofs 101 ◽

10.1201/9781003082927-2 ◽

2020 ◽

pp. 15-36

Author(s):

Joseph Kirtland

Keyword(s):

Proof Techniques

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Discrete Mathematics into K-11 and K-12 Grade Education

Journal of University of Shanghai for Science and Technology ◽

10.51201/jusst/21/05150 ◽

2021 ◽

Vol 23 (05) ◽

pp. 319-324

Author(s):

Mr. Balaji. N ◽

◽

Dr. Karthik Pai B H ◽

Keyword(s):

Set Theory ◽

Mathematical Reasoning ◽

Mathematical Induction ◽

Discrete Mathematics ◽

College Classrooms ◽

Underlying Principle ◽

Education Study ◽

Strongly Connected ◽

Proof Techniques ◽

K 12

Discrete mathematics is one of the significant part of K-11 and K-12 grade college classrooms. In this contribution, we discuss the usefulness of basic elementary, some of the intermediate discrete mathematics for K-11 and K-12 grade colleges. Then we formulate the targets and objectives of this education study. We introduced the discrete mathematics topics such as set theory and their representation, relations, functions, mathematical induction and proof techniques, counting and its underlying principle, probability and its theory and mathematical reasoning. Core of this contribution is proof techniques, counting and mathematical reasoning. Since all these three concepts of discrete mathematics is strongly connected and creates greater impact on students. Moreover, it is potentially useful in their life also out of the college study. We explain the importance, applications in computer science and the comments regarding introduction of such topics in discrete mathematics. Last part of this article provides the theoretical knowledge and practical usability will strengthen the made them understand easily.

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3. A case study in synchronization and proof techniques

A Calculus of Communicating Systems - Lecture Notes in Computer Science ◽

10.1007/3-540-10235-3_4 ◽

1980 ◽

pp. 33-46

Keyword(s):

Proof Techniques

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Proof Techniques for Cryptographic Protocols

Automata, Languages and Programming - Lecture Notes in Computer Science ◽

10.1007/3-540-48523-6_3 ◽

1999 ◽

pp. 25-39 ◽

Cited By ~ 2

Author(s):

Kevin J. Compton ◽

Scott Dexter

Keyword(s):

Cryptographic Protocols ◽

Proof Techniques

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Some Proof Techniques

Pathways in Mathematics - The Parabolic Anderson Model ◽

10.1007/978-3-319-33596-4_4 ◽

2016 ◽

pp. 71-84

Author(s):

Wolfgang König

Keyword(s):

Proof Techniques

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On Degenerate Truncated Special Polynomials

Mathematics ◽

10.3390/math8010144 ◽

2020 ◽

Vol 8 (1) ◽

pp. 144 ◽

Cited By ~ 3

Author(s):

Ugur Duran ◽

Mehmet Acikgoz

Keyword(s):

Bernstein Polynomials ◽

Stirling Numbers ◽

Bell Polynomials ◽

Euler Polynomials ◽

Exponential Polynomials ◽

Special Polynomials ◽

Summation Formulas ◽

Special Cases ◽

Proof Techniques

The main aim of this paper is to introduce the degenerate truncated forms of multifarious special polynomials and numbers and is to investigate their various properties and relationships by using the series manipulation method and diverse special proof techniques. The degenerate truncated exponential polynomials are first considered and their several properties are given. Then the degenerate truncated Stirling polynomials of the second kind are defined and their elementary properties and relations are proved. Also, the degenerate truncated forms of the bivariate Fubini and Bell polynomials and numbers are introduced and various relations and formulas for these polynomials and numbers, which cover several summation formulas, addition identities, recurrence relationships, derivative property and correlations with the degenerate truncated Stirling polynomials of the second kind, are acquired. Thereafter, the truncated degenerate Bernoulli and Euler polynomials are considered and multifarious correlations and formulas including summation formulas, derivation rules and correlations with the degenerate truncated Stirling numbers of the second are derived. In addition, regarding applications, by introducing the degenerate truncated forms of the classical Bernstein polynomials, we obtain diverse correlations and formulas. Some interesting surface plots of these polynomials in the special cases are provided.

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