Lynn, with just a few brief sentences, brought Elok down from heaven to hell. All the students present shivered uncontrollably.
"Advanced math is an extremely precise subject. We need to search for patterns within a vast and complex array of data, summarize them into corresponding formulas to simplify the algorithms and improve the overall efficiency of calculations," Lynn said, surveying every person in the classroom. He paused for a moment before continuing.
"While Elok's summary of patterns is not entirely wrong, it has too limited an application. If the exponent growth within the squares can be 2x, it can also be 3x, 5x, or 10x! This makes the pattern no longer valid..."
"However, this exponent summation formula applies to all exponent growth that meets the criteria!" Lynn snapped his fingers, and under the surge of magic, the complex formulas once again appeared before everyone.
[ Sn = a*r^(n-1) ]; n≠1;
Jenny, Pierce, and the others stared at the so-called exponent summation formula, pondering it deeply. Then they picked up quill pens and began to calculate, creating sequences of 2, 3, 4 times, searching for patterns and attempting to plug them into the formula.
With Elok's previous summary in mind and deriving from n≠1, Pierce quickly realized that the symbol referred to the exponent's multiplier. But why subtract 1?
Pierce bit his finger and plugged in the initial 2x growth pattern, ignoring the (n-1) part and proceeded with the calculations. He found that it worked perfectly, but the resulting number was negative.
So, did the latter part of the formula transform negative numbers into positive ones? But if it was a 3x exponent growth, the result wouldn't make any sense...
Pierce's brain raced, and he felt he was on the cusp of a breakthrough. What could it be?
Inside the entire classroom, students were all engrossed in their work, some scratching their heads, some pulling their hair, but not a single one chose to slack off.
Is the studying atmosphere at the Iyeta Academy always this intense?
Lynn found it a bit strange. These people were really passionate about learning.
The majority of the class went by quickly. Just when Lynn thought today wouldn't yield any results, a hand shot up high.
"Professor Lynn, I have some ideas!"
The one speaking was Jenny. After receiving permission, the young girl stood up and said, "In the summation formula, isn't 'a' the number placed in the first square, 'r' represents the multiplier, and 'n' corresponds to the number of squares, right, Professor?"
"Approximately correct. After class, you can collect your reward at the academy's entrance!" Lynn nodded in response. Though Jenny's explanation was quite vague, it was also absolutely correct.
Pierce, on the other hand, couldn't help but pound his chest and stomp his feet. After Jenny's reminder, he quickly understood why he was so close to solving it! Just a little more, just a little more!
After asking Jenny to sit back down, Lynn proceeded to explain what a geometric progression was, as well as its general term and summation formulas, and continued until he explained how each formula was derived.
The wizard apprentices below earnestly picked up their quill pens, wrote down every word Lynn said on their pages, and then tried altering the first term and the multiplier repeatedly to conduct verifications. The desks quickly piled up with various sheets of paper...
It had to be said that with the general and summation formulas in hand, the speed of calculations increased several times over. The more complex the equation, the faster the improvement.
Watching the enthusiastic students tackle their problems, Lynn couldn't help but sigh. Teaching was way too easy for him! If only this was the scene in all schools across the Federation, then the future of science and technology would be limitless.
***
The Arcane Mathematics class had quickly come to an end, but Elok and others were reluctant to leave the classroom. They continued to discuss the derivation of the summation formula.
"Jenny, from last night till now, how much has your control over magic increased?" a black-haired witch apprentice caught up and patted Jenny's shoulder, curiously inquiring.
"About ten percent?" the silver-haired girl thought for a moment and replied casually.
"That's a little more than what I achieved," the black-haired witch apprentice mumbled, without any envy on her face.
It was rumored that Elok had spent a sleepless night doing math problems and found that he had increased his control over magic by around twenty percent the next day. This news had caused quite a stir at the Iyeta Academy. So, this morning, any wizard apprentice without class came to hear what miraculous power this so-called arcane (advanced) math class possessed. She was naturally no exception.
The conclusion was quite clear; complex and intricate math problems could effectively enhance their mental faculties. The process of logical deduction, searching for and deciphering numerical patterns, was also interesting, at least more so than the tedious meditation.
Jenny paid no attention to the black-haired witch's words. She gazed back in the direction of the classroom, deep in thought. In the past six months, how many advanced math problems has Lynn done within the Society of Mystical Arts to achieve his current accomplishments?
***
"The ability to control magic can actually be improved by doing math problems?" Lynn couldn't help but hear the students' discussions, and it took him somewhat by surprise.
However, upon closer consideration, it made sense. His significant increase in power through a mental connection with an AI resulted from the overload mode substantially enhancing his computational power or, in other words, his mental strength.
This was crucial for wizards, as their ability to control magic was closely tied to the strength of their mental power. What frustrated Lynn was that this happened to be his blind spot in knowledge.
At least the process of forming magical patterns was somewhat similar to building muscle memory through repeated practice. For instance, picking up a glass from the table and taking a sip required determining the distance, calculating the right angle and force to grasp the glass, and finding the most natural arc for lifting it to your lips.
Under subconscious control, such a complex process could be executed instantaneously, without any hindrance. Spellcasting was no different. With extended practice, a mere thought could unleash incredibly complex magic.
But there was a prerequisite – the wizard's mental strength had to be substantial enough to provide sufficient computational power. Otherwise, the spellcasting process would be prolonged, revealing vulnerabilities.
Thinking this over, Lynn rubbed his chin, contemplating whether to solve a few calculus problems for himself...
Who knows, it might actually be beneficial.